Circulation control propellers for general aviation, including a BASIC computer program

Circulation Control Propellers

for General Aviation ,Including

a BASIC Computer Program .... ; I.T aback, A.L.Braslow,and A.J.Butterfleld The Bionetlcs Corporation i .

Hampton,VA.23666

c b_ Contract NAS1-16978 !_.

April 1983 "

g

•

KI Nabona l Aeronau ti cs and

Space Administration L m KIley Relemch C A nter Review for general release ;, p e l l 30, 1985 Hampton , Virginia 23665 ............

TABLE O F CONTENTS , P a ge 3.1.3 Ch o ice o f F li gh t C ond iti o n s ........... 8 I ( 3.2 De ri vat i ons ..................... lO 3.2 . 2 Ove rall P r ope]le r Cha ra cte ri s ti cs ........ 1 5 3.3 Pe rf orm a nce ....................... 1 8 3.3.1 Airf o i l Charact e ristics ............. 1 9 3.3.2 DesignMeth o dsand Design F act o rsC o nsidered . . 20 3 .4. 2 U s e o f L o w Ang l e o f Attack ........... 2 8 . 3.4. 3 Av o i d ance o f Su per so nic J et Ve lo city ...... 3 0 3 . 4 . 4 S e c ti on Effic ie ncy ............... 3 0 D m ,i i| ml -!

Page -_ T AB L ES ' -i 1 Charact e ristics of a S u p e rcritical Circulation Contr o l Airfoil ......................... II 2 Interpolation Co e ffici e nts for th e Charact e ristics uf _ 3 Characteri s tic s o f a Sup e rcritical 17 P e r c e n t T hick , 4 S u mmaryof Calc u lated R es u lt s for a S / C , - C / C Pr op e lle r . 22 6 Air F low Re qu irem e nts for a S / C-C / CPropell e rDriv e nby ' FIGURES !

- £ 2 D ra g Po larsf o r NASA S up e r criti c _i Airfoils ........ II _) 3 R atio o f Jet Velocityat AmbientPressureto Reference Ve l o citywith J e t Mome ntum Co e fficient.......... 13 { l 4 Comp u t e rG ene r a ted d ata f o r C o m p arison Ev al u ati on o f i P r o p e ll e rs........................ 23 1 I 6 D ra g Pol ar s f o r S / C and S l C - c l cAirfoil s wlth P r ope ll e r !

Ope r a ti ng B ounda ri es ................... 2 9 ) t • !

] I ii --_

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CI R C U LA T ION C ONTROL P ROPELLERS FOR

G ENER A L A VIA T ION , INC LU DIN G

A BASIC C OM P UTER P R OG R AM

I I. Taback,A. L. Braslow, and A. J. Butterfield The Bionetics Corporation Hampton,VA. 23666 i ' SUMMARY .]

I A st ud y h as be en m a de to determinethe fe_ s lbility of replacing J variable-pitch propellermechanisms with circ u lation-control propellers _ comp ut e r p r og ramwritten in BASICand placedemphasison comparingthe i i aerodynamic performance of circulation-control propeller s with on generalaviationairplanes. The s tudyu s ed a s pecially-develo p ed !"i _'_ c o nventional propeller s .

Th e aer od ynamic performance of circulati on -c o ntr o l pr o peller s is c o m p aredwith th e aero d ynamic perfo rm ance o f b o th v a rlable-pitch an d flxe d -pitch p r o pellers again s tthe re qu irement s o f a 1 6 00 Kg ( 36 00Ibs) e s ingle-englne aircraft. The applicati o n o f a c irc u l a ti o n-contr o l pr o peller with a s upercritical airf o ilwas f ou n d f eas ible u n d er repre s entative de s ign c o nd iti o n s . All p r o peller s ha d a ppr o ximately the m I i I i I

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sa mep erf o r m an c e a t h i gh spe e d cru i s e (des i gn cond it ion). At low spe e d, t he performa nce of the c ir cu lati on-con tr o l p r ope ll e r wa s h i ghe r than th a t f o r a fi xed p i tch p r op ^ lle r but lo w e r th a n th a t f o r a varia ble p i tch p r opelle r .

I t a ppe ar s f e a s i ble to r _ p la ce va riah le-p i tch p r opel l e r s wi th !

circ u lati o n-c o ntr o l pro p e ll erson single eng i ne aircraft o r o n I

m ulti -e ngin e aircraft whichhaveth e irpr o p e ll e r s on a co mm onaxi s

(Tractor - Pu s h e r) . Th e e c o n om ic so f th es e r ep lac e ments requirea s tudy fo r e a c h s p ec ifi c aircraftapplicati o n.

i ) L ) !

i 1.0 I NT R O DUC T ION !

i T h e fea s ibility of us ing circ ul ation-contro l (C / C)airfoil s { bl un t- b a s e d airfoil sut ili z ingt h e Coandaeffe c t)for generalaviation airplanepropeller s i s being apprai s ed. Fuel con s umption and / or total i life co s t advantage s might oc c ur throughreplacement of variable-pit ch propellers wit h fi x e d -pitch C / C pr o peller s . The requiredchangesin _ propel l eraerodynamic characteri s tics throug ho utthe s peed range o f t h e airp l a n ec oul dbe o b tainedthroug h change s in the ma ss -fl o wrate of t h e bl ownjet. A s implified analytical approachwit h hand cal c ulation s provi d e d a first-or d er e s timate o f prope l ler aer o dynamic performance wit h e ll iptical and s upercritlcal ( S / C)circ ul ati o n-c o ntro l ( C / C) airfoils(ref.I). These re su lt s in d icated that a S / C-C / Cairfol l for w h ich d ata becameavailab l e appearedaero d ynamica ll y s ui t a b lefor us e in a p r ope ll e r. T h l s s t ud ywa s u n de rta k ent o m o r e a c c u rat e ly de f ine th e 4

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c h a r ac t e ri s tic s o f C / C p r ope ll e r sb y a mor e r e f i ne da nalytic a l ap pr o a ch ] wh i ch u s ed a sp eclal ly- developed c om p u ter prog ra m writteni n B ASIC. _ Th i s p rog r a m i s pre s ent ed in t he Appen d i x . A br i e f assess me n t w as ma d e ' i , o f the re qu ir eda ir c omp ress o r a nd th e in s tallation c o n s i d erati ons .

" , . As par t of the a ss e ss ment of a S / C - C / C pr op e ll er,perf o rmance > com p ari s ons were made for a selectedairplanewit{, S / C variable-pitch :- a nd S / C fi x e d - p itch pr op ell e r s . Altho u ghnone o f the p r o peller s were - optimizedfor m aximumperformance, the basic relativecharacteri s tic s !

sh o ; ll d be valid. The pr o peller s were de s ig n ed for a high- sp eed i s teady- s tate flight c o ndition of a typicalsingle-engine airp l ane.

Fu rt h er c o m p aris o n s were ma d e at a l o w- s peed flig h t conditi o n for s t e a d y- s tate perfo rm ance and f o r rate-of- c limb o r acce l erati o n _° pe rf orm a n ce .

- ,_ T hi s s t ud ywa s initiated b y Mr. H. D ou glasGarner o f th e L ang l ey 1 ,i R e s ear chC e n t e r,w ho p r opos e d t h e c o nce p ta s a re sul tof hi s work with fl u idic d evice s . The study received s upport fr o m Mr. Eman u el B o xer, " i Di s tingui s hed Rese ar c hA ssoc iateLaRC and the analyticsoftwarewas • a da pt ed fr om a pr oc e du re dev el op e d by Mr. WilliamH . Ph i l li ps , Di s tingui s hed Re s earchA ss o c iat e LaRC,Mr. Wayne H. Bryant o f T he LaRC :_ " i pr og rammed th e techni que in B AS IC,primarilyf o r this s t ud y, ho we v erthe ) p r og ram c a n suppo rt o th e r generaldesign evaluation s . The pro o ram

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pr e pared b y Mr. Bryantapp e arsa s the Appe n dix. I

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I i ORIGINAL PAGZ I S , OF POOR QUA LIT Y i 2 . 0 SY H BO L S ANDCO EFF ICI ENT S : a In du ce d a x ial v e lo cityrati o B N u mberof propellerblade s c Propel l erchord,m (ft) cd A irfoilwa k e drag coefficient I j c£ A irfoillift coefficient I c_ Blo wingM o me n t u mc o efficient, ... m V_ I I / 2P= V i 2c i D P r ope ller d iameter,m (ft) i HPa er o P rop el lera e r o dynamic h o r s e p ower, 7 4 6 watts " 550 ft-l b s ] : HPc C o m p re sso r ho r s e p o wer, 746 watt s [5 50 ft-l bs ' !

HPpc P r op e l ler-c omp re ss ion ho r s e po wer, 74 6 watts 550 ft- lbs] HPu U s ef u lh o r sepo wer . T V ®, 7 46 watts [ 5 5 0 ft- lbs ] !

HP t o ta I Re qu ir e d ho r sepo w e r, 74 6 watts [5 5 G.f_tt-l bs ]

L s ec ]

HPav a i I Av ailable ho r s e po wer, 7 46 watt s [_$ 5 0 ft - l b s ] _

L ]

h Altit u de, km ( ft) L / D Ratioof Lift Forcet o Drag Forcef o r an airf o il B lo wingma ss f lo w p er un it sp an, k g / s e c / m (slugs / s e c / ft) I n P r op el le rr o tational sp ee d, r ev / s ec I P S t a ti c p re ssu r e N / m 2 ( l b / ft 2) P t To t a l p r essu r e , N / m 2 ( l b / f t 2) P = A m b ie n t p re ssu r e, N / m 2 ( lb / ft 2)

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t ORI G INAL PA G _ Ig O F PO O R QU A LITY Q P r opell er to r que, N-m ( f t - lb) R U n i ve r sal g as c o ns t an t, m2 / s e c 2 °K ( f t2 / sec 2 °R) .

Al so: P r op e ll er ra d i us at t h e ti p o f t he blad e, m ( ft) (RN) Re y noldsnu m be r ba s ed on c ho r d , cl V l p- r P r ope l l err ad i usat a r ad i a lstati on ,m ( ft ) T Stat ic tem pe r atu r e, °K ( ° R) Also: Thrus t, N (lb) V Vel oci ty , m / sec ( ft / se c ) V F r ee s tre a m ve l o ci t y, m / se c ( ft / sec) W Airplane g r os s weight, kg (lb) Ang l e o f a tt ack , de g ( S ee D ia g ram b e lo w ) B P r opelle rb lad ean gl e , d e g ( S ee D i ag ram3 elo w ) n P r op e l I er E f f i c i en c y X Advance Rati o , V _ , (S e e Di ag r a m belo w ) 2 _Rn' ® Ambi e nt v i s c os ity, N s e c / m 2 (Ib sec / ft 2) p Density, kg / m" (sl u gs / ft 3) p® Am b ient dens ity, kg / m 3 (s l ugs l f t 3) ._ .

Ang l e o f advance ,t an "IF V ® l , :_" (See D i agr a m be l o w ) -; v !

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ORIGINAL PAGE I S OF . POOR QUALITY Subcrlpts h Blad e hub stati o n i B l a de elemen t ra d ial stati o n , {0 t o 20) {NOT E : Units for T and Q with s ubscript I ar e pe r unlt s p a n) j Oe t ) P r o p e l le r Blad e De finiti o n o f Tems | 3 . 0 RESULTSA ND DI S CUSSION 3 .1 C ho ice so f Ana l y s i s C o n d i t i o ns 3 .1.1 Ch o ice o f Airp l ane The d esign an d c o mparis o n s o f prope ll erperf or mance were ba s e d u pon app l icati o n s t o a specific m od e l generalaviati on airpla n e. A s u rveyof ge n era l aviati o nairp l anes(ref2) s h o we d the f ol lowingrange s for maxim u m s pee ds .

(a) S ing l e Engi n e,Fixe d Pitch 5 9 .2-77.1 m / sec (1 9 4- 2 5 3 ft / sec) (b) Sing le Engi n e,Variab l ePitch 6 6.8- 9 7.6m / s ec (21 9 - 3 20f t / s ec) (c) Twin Engine,Variab l e P itch 8 7.5-12 3 .5 m / sec (2 8 7-405ft / sec) One o f the we ll e s tab l ishe d m od e l s o f s ing l e-e n gi n e ge n era l aviati o nairp l a n e ss howe d a maximum s pee do f 82. 3 m / s ec ( 2 7 0 ft / sec) which i s ab ou t t h e maxim u mf o r which a fi x e d pitchpropel l ermight be use d . Thi s airp l anewa s s electe d becau s eit s perf o rmance o ver l appedthe ra n gef o r b o th fixe d a nd variab l epitch pr o pe ll er s . The aircraft s e l ecte d ha d a maximumweight o f 1 6 00 kg ( 3 600 I b s ) an d use d a 3 bl a d e d variablepitch pr o pel l er drivenby an un s upercharge d e n gine. A lt er n ate m odels o f t h e airplaneare available , it h su p e rc h arge d eng i n e s.

ReferenceI presentssome of the specificcharacteri st ic s of thi s airplane.

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3 . 1 . 2 Ch o ice o f P r ope l le rAirf o il ) ) | A r esul t fr o m t he p r ev i ous stud y ( r e f 1) i ndi c ated supe ri o r ) pe rf o rma nce f o r a p r ope l le r w h ic h u t il l zedC / C-su per c rl t i c a l a l rf o l ls a s i ' co mp a r ed with t he p r ev l ousl y anal y zedC l C -e111 ptlc a1 al rf o l ls.

A v ai l a bl e da ta f o r S / C - C / C atrf o i l s ( r e f 3) w e r e the r e f o re used f o r t t h i s stud y . I n t he p r evious anal y ses, p r el im in ary dat a w e re p r ovtded b y % _J the David Taylo r N a val Ship Research and D evelopmentCenter w i t h t he "4 , drag ch a r ac t er i s t ics ob t ained on a 1 7 percent chord t hick S / C a lrf o l l reduced t o values equlv a len t t o a 1 5 pe r cen t chord t hick S I C al r f - " - ¢ direct compa r ison t ;I t h the previousl y t e s t ed 15 percent chord t : * + ellip ti cal airfo i l s . Fo r t hts s t udy, no t hickne ss co rr ec t ion w c _ . _ - ; The pro babl e u s e of t h in ne r airf o ils i n a n a c t u al l,, u _el er a ppli ca ti on Is expe ct ed t o have an i nsign ifi c a n t e ff ec t on t he p r u ve lle r .

3.1.3 Cho i ce o f Fltgh t Condi t ions - - A high-speed c r uise f ltgh t condition o f 82.3 m / sec (270 ft / sec) a t 3 .05 k m (10,000 i t ) a l t t t ude w a s selec te d a s th e de s ign poin t for the - _ p r opeller s . Although t he pe rf ormance of t h e a ir pl a n e should be computed .M _j at man yf ligh t conditions, a sele c ted low-speed f ligh t condi t ion o f 38.1 / m / s ec (1 2 5 f t / sec) a t se a level should p r ov i de a mea n ingful indica t ion of off-design p r opelle r pe r fo r mance. R e l a ttve propelle r efficienc y in ; stead y -state low-speed c r u i s e and r ela ti ve t h r us t ma r g i n av al l a ble fo r c l imb o r accele r ation w i t h the g i ven engine p r ov i des a useful compa ri son o f t he p ro pel l e r s. A pr ac ti c a l design mus t e valua t e t he entire r an g e o f t : E :" fli gh t condi t ions i nc l ud i n g t a ke - o ff pe rf ormance , o b stac l e c l ea r anc e, I _ " ma ximu m speed etc. Thts lim i ted compa r ison investigated only tw o flight conditions.

I 3.1.4 S y stem Desc r iption !

The s y s t em a n al y zed, Figu r e 1, re p r esents the s im p l est concept that

i

could be ap plted to t he circulation-con tr ol p r opelle r . A t r tnducted !

from an tnlet at _ . ts fed to an engine-d r iven c om p re sso r . Thts atr ts !

J f urnished to t he propelle r hub vt a ducttng, valves, and rotar y seals. ] .i . ] The propelle r p ro vtdes addition a l compressionb y cent rif ugal pumptngso I l that a vartable press, : _ head exists f rom the hub to ti l e outboard I m,,' ........................ _o_ . . _; . j , g_ . _ , % , e r " ' I = _ . _ r .5 . . _ ' _ -- I O R I GIN A L P A gE I l l _ ; OF POOR Q UALIT y B l o wi ng Edge -_ Jl J I ii Plen u m S haft S e al s Flow Con tr ol V al ve !

C omp r esso r P Air I n ta k e

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AirFr om P le n u m. _ __ B lo win g Slo tHeight. ! s °'°OI 2 c i!

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_ , _ . ,T, , ............. _ ' " ....... "___ k T h i ckness . I' " Blo wi ng Edg e D e ta!1 _ _.J _ is 0 . 0188c i Fi gu r e 1, C ir cula ti on Con tr ol Pr opeller S ys t e m j _ . _ _ -- I nnnnn . . , _ " ' • '" __._i' ___.-_' ,"_ ,_,.__.

I end of a single b lo w ing - s l o t plenumc h a mber. T h e ex it slot ts assumed t o b e th e ma j or flow res t r icti on i n th e s y s t em s o that t he pr essure 'I gr a d i ent t n the pr o p eller pl enum I s c al c u l ated fr om th e h y dros t at i c equ a tions fo r p r ess ur e equilib r iu m . Th e r adt a l c r oss-flo w s w hich may _ ex i st tn the e xt t slot and exhaust have been i gno r ed i n t hts s t ud y .

3.2 De r iva ti ons i 3 . 2. 1 Ae r od yn a mic Rel ati onsh i ps t T he prope l le r se ctio na er od yna m i c c haract e ri s t i c s a re desc rib ed by i th e s t anda r d c£ and cd val ues a s f u nction s of ang l eo f attack_ for th e !

non - b low np r ope l le r s. Circ u lation contr o lp ro p e ll e r s r e q u ireth e I ; " addi t ional pa r ame t er of mo me n t um co e ffici e nt . Thes e re l a t ions h ips a re shown gr a phi c ally in F i gu r e 2 for t h e s v pe r c r l ti cal ]7 pe r c e n tthic k airfoil,and the s a me airfoil m o d ifi ed for trailing - edg e blowin g . T h e ( polars shownwer e linearl ze d ov e r s m allangl e- of - attackrange s (usuall y 3 deg r ees) with the nu me ricr esul t s,ex tr a p ola t e d, shown in Ta b les 1, 2, and 3 . T h e so ft w ar e des c r i bed in the Ap p e n d ix linearly i n t e r pola t es b e t w e en th ese t a b ul a t ed values t o o b t ain sp p ct ft c va l ues o f . ._ t he ae r od y nam i c ch ar acte rt st t c £ ,.

The mome n t u m coeff i c i ent a t an y sect i o n i s r e l a t ed to the ple n um tota l p re ssure as f ollo w s: V j l - V 1 (26.4) (c _ t) _ (1) Thts rel a tions hip t s d e r i ved f r om F i gu re 3 (reproduced fr om ref 1). ' ) S a mle poin t s compu t edf rom t he abo v e eq u ati o n ha v e b een added t o t he i ort g tn a l figure. , j_ .

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l I I I + ,. A J_ m ORIGINAL PA(;IEIS OF P OOR QUALITY Ta bl e 2, I n ter pola ti o n C o efficient s for th e Charact e ri s tic s o f a S u percritical Circ u lati o n C o ntrolAirf o il(ref 3 ) c( a nd c d = A + Bc u + {C + Dc u ) - a % U : _ C o e fficients t o d etermi n ec_ , " O& ] O& u A B C D l o wer u pper - 1 2 - 9 - 0 . 68 53 . 5 0 . 26 -1 . 0 - 9 -6 - 0 . 4 2 52.5 0.27 -1 . 0 - 6 - 3 - 0. 15 51 .5 0 . 28 -2 . 0 - 3 0 +0.1 3 49. 5 0.2 5 -0. 5 0 0 +3 O.3 8 49.0 O. 2 8 - 3.50 +3 6 0.66 45 . 5 0.26 - 5 . 50 6 9 0.92 40 . 0 0. 2 4 - 8 . 00 9 12 1.16 3 2 .0 0 . 17 -9 . 50 12 1 4 1.33 22.5 0 . 07 -5. 50 14 > 1 4 0 0 n 0 Coefficients to d etermine cd - 1 2 - 9 0 . 009 -0 . 4 0 - 0 .0 01 0 . 000 _ - 9 -6 0. 008 - 0.4 0 0.0 0 00 0 , 0 0 0 - 6 " - 3 0 . 008 - 0 . 40 O . 0 00 9 - 0 , 0 2 5 - 3 0 0 . 0089 - 0 .425 0. 0011 +0 .0 20 0 +3 0 . 0100 -0 . ;; : 5 0.0031 0.0 4 0 +3 6 0 . 0 1 3 1 _ 0 . 3 6 5 0 . 00 2 4 0 . 075 6 9 0.015 5 : " 0 " 29 0 0 . 0069 0 . 000 9 12 0. 0224 -0,290 0. 0035 0. 62 0 12 14 0 . 0259 -0 . 270 0.0077 0,27 0 14 >14 sin _ s i n a s i n (_ stn =

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ORIGINAL PAGEI I

O F POORQUALITY

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O RIGINAL PA_ , Y [ 3 OF P OO R QU A LI T I ' T h e B er n o u lli i n c omp r ess ib l e r e lation s hip b etween ve locity a n d pr e ssu r e ts:

(z)

Pt.

= 1 / 2p.(Vji ) 2+ P _ T hi s e qua ti on gi v e s the j e t v e lo cityw h e n the se cti onpl e nu mt o ta l pre ssu reair is expa nd edt o free- s tream static pre ssu re.

The plen u mpre ssu reat any s tati o nis relatedt o t h e hub pres su re a s sh o w n be l owby the is o thermal hydrostatic e qu ati on whic h acc oun t s f o r ce n trif u gal accelerati o n as: . z d Pt = P( 2 _ n) 2r d r ( 3 ) dp 1 B_-t =RT ( 4) --, .

d_pp = (_2_ n)2r dr ( 5} :"_" " p R T : .: ,| I n tegrating fr o m the h ub to t h e ra d iusat stationi _", ,!

: P i Ei _hh= e " e (6) i i

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T he h u b pres su re c a n be adju s te db y use o f t h e c on tr o lvalvew h ic h ", i op er a t es i n s e rie s with th e c o m p r es s o r.

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Th e loc a l alr s tream veloc ltyat r a d i us r i s t h e ve ct o r su m o f t he !

I f o rward_ nd r o tational v e loci ti es: ' i Vi . + . (7 ) !

[V J ( 2 _ri n)2] _ '!

° 1 4 , -

O Ri G iN AL PA O_ _ i

O F P O OR QUALIT Y T hi s eq u ati o n do e s n o t ta k e into acc ou ntthe inf lo w velo citi es in du ce d by t h e propeller b u t t h e c o rrections are too small to be of c o nc e rn.

C o mbiningthe above relationships, an expressi o ncan be derive d - betweenthe momentumcoefficient and the hub pressure: _ 2 RT P he I (8 ) c " i (26.4 ) 2 L-_ VZ + ( 2 _rin ) The temper a ture T to be used in this equation is the p r opelle r i tem p erature; h o we v er,at the lo w speedcon d itions evaluate d in this i re po rt,the fr e e-stream s tatictemperature can be substit u ted.

3 .2. 2 Overall P ro pe ller Characteristics Prope ll erthrustand torqueare d efinedby the fo llo wing r e l ati on s hi ps: .; Ti =B'r dT = ½P®V oo2 F1+__a7 2 .

Ls_ n ,] B c(c_c os ,- c ds i n ¢ ) (g ) "

Bc (c t s i n¢ + CdCOS #) ( 10) acc o unt ijl These ar e t h e c onven ti o nal p r op eller se cti o ne qu ati o n s and ( f o r the in d ucedflow at each se cti o n. To c o mp u t e the overallthru s tan d ) i : torque,the sectioncontributions are s ummed using S imp s onsrule. T he metho d u s ed for computing the inflowby iterationis describedin the Appendix an d i s adapted from a methoddevelopedby Larrabeeand F renchat

1 5

" I ORIGIN A L P AeE IO U P O OR QUALITY ' d t he M a ss a chuse tt s I ns tit u t e o f Technology.

I n add iti on t o t he s tri p i n t eg r a ti on me t hoddesc ri bed a bove, use wa s made o f an analytic so ftwar ep r og ram d ev eloped by Wi ll iamH. .; Phi l lip s ,(Di s tingui s he d ResearchAss o ciate,LaRC),t o s ec u refir s t aPF imations f o r efficient propellerchord distributions.These relationships are also basedon work by Larrabee(ref4). In all the : , comp u tations made, the analytican d s trip integrati o ns f o r the same pr o peller agree d t o within 1 perce n t.

3 .2. 3 System Efficiency Th e ove rallefficiency o f t he p r opel lersystem is computedby divi d ingthe usef u lw o rk d o ne by the sum o f the w o rk re qu ire d t o r o tate t he pr o p e ll e ra nd t he w o rk requiredto compressthe free-stream air to !

thG p len u m p r essu reat each propellerstation.

The requiredmass flow per unit lengthof propelleri s , (ref I) ....

= ( Vi ) 2 " = / (11 ) • mi clJici2Vji T h e ho rs e p o wer r eq uired pe r f oo t o f p r opel lerradius to pump a mass _ of air from the hub t o a radialstationis: i m

1 !

HPpc i = _i ( 55 0) • _. • )

.)

J

t l 16 .

,, ., . . , +,. , , • OR I GI NAL P ; ;3_ . E l _ OF PO O R QU A L I T Y " Fo r a pr o peller with B blades, th e express i on ca n b e wr i tt en f or ea ch ra d i us s tati o n r : , I

, / % ,1 - ( ' > '

To fi nd the ov erall h o r sepo w e r r e qu ir ed, the se c t i on h o r sepo w e r i s ¢ .

su mmed u sin g $ tm psons r u l e. The ho r s e po wer f o r t he e n g i n e - d ri ven compre sso r i s d e te r m i ned f r om th e requ ir e m ent that the total mass flo w i s compr e ss e dfrom the a m b i entpr e ssure t o the pressure a t the p r ope ll e r i h ub . T h e t o tal ho r sepo werI n t o th e p r op ell e r c o nsi s t s o f th e w o r k f or a er od y n amic t o r quep l us the w o r k re qu ir ed t o ce n trif u gally pump t he a ir, _ a s well a s t h at p erf o rme db y the c o m p re sso rt o supp ly hub p r essu re.

H P t o ta I -- HP a e r o + HPp c + HP c . ,, I - 2 ¢ ' ' : , I HP t o tal 5 50 = _ + HPp c + HP c (1 4 ) ; !

& # T h e us ef u lw o r k do n e b y th e p r ope ll e ri s th e t h r us tm u lt ip lie d b y airplane ve l oc ity, a nd in h o rse po w e r is : I I I TV _ H P = = (15) , !

!

1 7 -'" t I = ORIGINAL P A GE iS * _ OF POOR QUALITY The s y s t e m eff i c i enc y i s: TV = / 550

n - (1 6 )

_ 0 + HPp c + HP c T he a bo v e e qua ti ons, an d o th er ancillary relation s hip s to d e fine a t mospher i c p r ope rt ies versus al tit ude, local Re y no l ds and M a ch numb er s ) and ot he r pe rti ne nt fa c tor s h av e b een mec h a n i zed in BASIC a nd ar e d e s c r ib ed i n the A pp e n d i x. The p r og r a m i s useful for des i gning an y pr ope ll e r f o r w h ich th e se cti on a e r od ynamic c h aracteri s tic s can b e s tatedversus apgle of attack in a look-uptable. In a dd iti o n,the p r og rami s capa b le o f varying p ara me ters su ch a s e ng ine r o tati o nal sp ee d or b l ade helicalangle an d providescro s s-plot s for trend analy s i s .

re P ertine n t r esu lt s of t he c o mputati ons ma d e f o r thi s s t ud yare p re s ente d ._- b e lo w . : 3 . 3 P e rf o rmance i Th e des i g n p o intf o r all o f the p r ope ller s wa s 8 2. 3 m / se c( 2 7 0 ;k_ ft l s ec)at 3. 0 5 km ( 1 0,000 ft) a l tit u d e an d t h ey w e re t h en analy z edf o r _ * _ .

,,| lo w s peedflightat s ea lev e l . N o attemptwa s made t o o ptimi z eth e i p r o pel l er d iam e ter o r n u mb e r o f b la d e s. A 1 .8 3 m (6 ft ) d iamet e r 3 i

I

b l a d e d pr op eller wa s used f o r all c omp ari so n s. The li s tingbe lo w i J s ummarizes t h e de s ignand off-de s ig n flig h tc o nditi o n s c hose n p l us l I pe rti nen t alr pl an e an d eng i nep arameter s: I .!

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o 1 8 I ' I Design (Cr uise) Off-Design (Sea Level) Altttude,h 3.05k m (10,000 f t ) 0 Vel o city, V. 82 . 3 m / sec ( 2 70 f t / sec) 38 . 1 m / sec (125 ft / sec) Th r ust r equ ire d, 1441N (324 lbs ) 1544N (347 lb s) stead y state Engi ne r p m, 2500 2700 • (f u l l thr o ttle) Eng i n e HP, 188 285 • _ ( f ull th r ot tl e) 3. 3.1 Airf o ilC ha r ac t e ri s ti cs , T he ae r od y n a m i c cha r a cteri s tic s me a s u r ed f o r S / C - C / Ca irf o il (con fi gu r a ti on 5 o f r e f 3) a re sho wn i n F i gu r e2 f o r a r ange o f blo wi ng I m o me n t u mc o effi c ie n t a n d a n gle- o f-attack. T h e drag c o efficient s pre s ente d are wake d rag c o efficient s t h at inc lud et h e m omen t u m o f the blo w n J et. T h es e d iff e rfr o m t he c oe ffi c i e nt s u se d i n t he i ni tialstu d y _:_ ( ref 1) , w h er e , f o r pu r poseso f a irfoil co m pa ri son , t h e w ake d r ag _ : t c o efficient s were c o nverte d t o d rag c o efficient s that i n cl ud e d a d ra g equlvalen t o f t h e b lo wi ng pow e r r eq uir ed. I n t hls s t ud y, t he p ow e r _ t _.

r equ ire d t o blo w t h e a tr t s s e pa r ate ly a c c oun t ed f o r a nd cha r ged t o the | ; _' : : a ir p lane eng i ne. Th i s me t hod t akesac c oun t o f t he tr igono metr i c !

!

r ela ti on s h i ps r equ ire d t o co m pu t ep r op e ll er e ff icien cy .

I n t he angle-o f -a tt a c k r an ge o f htgh L I D (abou t 30 f o r the S / C - C / C i I ai rf o i l), t he L / D at no blo w ing is 53.8 and inc r ea s es wi th blo w tng.

The ove ra ll e ffi cienc y o f t he at rfo t l ts 11 m t t ed , ho w eve r , b y t he ene r g y : r equi r ed t o comp r ess t he at r fr o m a m bien t p r essu r e to t he plenum pressu r e at t he J e t . As at y ptcal exa m pl e o f sectton e ff icienc y , t he charac t e r ist i cs o f the S / C -C/ C section w e r e eva l uated at an a dvanc e [ r a t io o f 0. 6 9 f o r a fi xed 3 0 angle o f att a ck w tth va r iou s val u e s o f c , .

19 ., _ . :: .

k ,v v¢ _; _ T he s ecti o n e fficie n cy at c_ = 0 o f 0.96 wa s reduc e d t o 0.95 a s the c_ _:_ increa s ed from 0 to 0.02. Largerval u es of c_will f u rtherdecrea s e { - _ the s ecti o nefficiency e v e n th o ugh t h e aerodynamic L / D for the section , _ ._ it se lf i s increasing. For applications where the jet velocityi s not .

i. _ o therwiselimited,it is possiblet o use momentumc o efficients u p t o i "i _) about0. 0 2 withoute x ce s sivelo ss es in efficiency.

Ji 3.3.2 DesignMethodsand Design FactorsConsidered The numberof bladesand propellerdiameterwere held constantto st u dy the relativeperformance of the propellers describedbelow. The f diameterwas selectedto maintaina low tip speedwhich permitted an additional jet velocitynear the tip. In each case,an angle-of-attack -, distribution was selectedand the analyticminimum-loss chord distribution determined. The chord distribution was scaledto achieve the r eq uiredthr us tat the high-speed designpoint. I Th reeangle-of-attack d i s tributions were investigated:a nominal20 1 and 4 0 uniformhub to tip and a "twisted" distribution of -120 hub to i ' +50 at the tip. T he small anglesof attackwere selectedbecau s ethey l_i - w e r e l o catedi n th e r e gionof maximumsectionL / D and providedfor a largerangeof operationbefore stallat low forwardspeed. The "twisted" di s tribution was selectedto give rea s onable performance at the high- s pe ed d es i g n p o inta n d t o minimizestallas m uch as po ss ibleat the off- d e s ignpoint. The summarybelow o utline s the d e s ign p roced u re_

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used t o m a t c h p r o p e ll e r pe rf o rmance t o the a irplanethru s t requirement s . )

}

.i

b

J

i g _ p ° . ,_ h_ 4 J I k " ._ L _j _ Pr ope lle r Typ e Des i gn Point O ff -Design : 3.05 k m (lO000 ft ) S ea Leve lCr u i s e _j S I C A n alytlcml n lm u mi oss F i x e dPi t ch - va ry cho r dd i s tri bu ti on e ng i n e r p m v a ry h u b s etti n g Va ri a bl ePit ch - S / C , C / C, with Match cA at O. 7 R t o S et c_ = O. Vary blo wi ng pl e nu m abov e S 7C des i gn, eng i ne r p m t o 0.7R a nd no j e t Ra ti o cho r ds t o

fl

v e loc tty re s tri c ti on s ec u r e r equ ir ed th r us t .

:i S / C, C I C with bl o wi n g A na lyticminim u m Se t c_ = O. V ary 0.9 son i c vel o clty d i s tri bu t ion t plenu m t o ti p and loss c ho r d e ng in e r pm : re s tri c ti on i ! E a ch ca s e in t he p arametric st ud y ( 1 0 t o tal) p r oduceda print ou t I b l o w n i o f t he p r ope ll e r ch ar a c teristic s , p l us Je t c h ar a cteri s tics f o r " p r opell er s . T a bl e 4 sho w s a ty p ical p rint ou t. I n a ddi ti on, t h e p r og ra m ge n erate d a n u m b er o f cr oss pl o t s . F ig u re 4 s h ow s e x am pl e s . T h e A pp e nd ixc on tai nsp rint- ou t s o f propel l er c h ar e ctcri s tlc s f o r the vari ousdes ign ss t ud ie d .

F o r the o ff-de s lgnc o n d iti on , the p r op e l ler-e n gi n e co m b i n ati on wa s eval ua t ed t o d ete r mi n e t h e e xcess t h r us t w h ich cou l d b e ma deava il ab l e !

above t ha t r equi r ed f o r s t ead y- s t a t e f ltgh t . The excess t h r us t , use ful f o r ra t e o f c l imb or accele r a t ion , w as li mite db y t h e f u ll - t h r o ttle eng i n e horsepo w er a t 27 0 0 r pm o r b y t he m a xi m um th r ust capabilit y o f t he spect f tc p r opelle r a t an y r p m up t o 2700.

3.3.3 Propeller Cha r ac t eristics A summa ry o f th e opera t ing cha r ac t eristi c s o f the f tnal C / C and Lt u, , 1 p r ope ll e r s ( V P and FP) investigated ts presen t ed tn F i gu r e 5 and |

2 1

" ' " OR | Q INA L PA G E | g

" _ 7_ , ® 7_

• I / _

" " " 1 " 71 "> ' ;

/ / I "_

/ / I _

• " | / / I _ '_

,_o u "- - , L I_., o

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23 " L t he p r o p elle r effic tenc i es i n s t e a d y -s tat e cr uise ar e pr es e n t ed i n T a bl e 5 fo r bo t h t h e high-sp ee d a nd l o w- sp ee d f li gh t cond itio ns s e l e c t ed.

Tabl e 5 , Ca lcu lacl ons o f P r opel l e r E fficiency P r op eller T y pe Des i gn Po int O f f Des i gn Poin t 82.3 m / s e c at 3.05 km 38.1 m / sec at Sea Leve l (270 ft / se c at lO , O00ft) ( 1 25 ft / s ecat S e a Le v el) j V ariabl e Pitch 0.897 at 2500rpm 0.784 at 27 00 rpm Nar r o w Chord F i xed P itc h 0 . 89 7 at 25 00r pm 0 . 620 at 2100 r pm _ Na rro w C hord S / C-C / C 0.886 at 25 00rp m 0 . 77 7 at 1800rpm W ide Ch o r d wit h .

blowing t o t i p, su bs on i c jet .

Fo r t he h i gh - speed c r u i se des i gn cond iti on (F ig u r e 5a) t he cho r d of each p r opel l e r ( C/ C and unb l o w n) wa s es ta b li shed as desc ri bed abov _ .+h • (section 3.3.2) to provide t h e thrust required fo r c r u i se a t the t)_j_ recommended eng i ne r pm o f 2500 for susta i ned ste a d y - s t a te fli ght, ( indicat ed asQ ). A val ue o f c) = 0. 00 2 5 at 0 . 7 R w a s se l ected f o r th e i C / C p r opeller pr i o r t o es tab l i shment of t he C / C ch o r d t o ma intain ) s. b sontc blo win g, T h e print ou t as Ta bl e 4 shows th e vari a ti o n o f c p L (a n d j et v e l o ci t y w he n expa n ded t o a mb i e nt p r essu r e) a l ong the span.

!

The efftc t enc t es at h igh - speed c r u i se a r e n e arly th e sa me (abou t 0.89) i !

fo r all three prope ll e r s (see T a b l e 5). Th i s i s n o t u n expected as all + a re opera t i n g a t a selected angle of a t tack t hat provides h tgh L / D ra t i os.

j.

O F PO O R QUALITY t " -" 1778 Al1 P r op e lle r s ! , (400) -' _ J . . . .. n =0 .3 9 . .

! O RIGI N AL PAG _ |_ i

. | = j _ J

. Thrust Requ i red _ I _ W -1600k q( 3600 lbs) _ . - - _" 889 i " _ . _ ' = (ZOO) _ Thrust Requ i red

m

W -1333kg (3000 lbs)[ S / C - C / C Wi de Cho r d ' _ - , ® c_ = 0 .00 2 5 a t 0. 7 R I

l IB c u = 0

I

i

O - I | (a) High Sp e ed C rui se: 8 2 .3 m / sec at 3.05 _ , ( 270 f t / sec at 10,000 f t ) 44 4 7 (1000) T .... Th ru s t Ava i lable F ul_ Th r ottle n S / C - C / C Wic)a Chord ^ = = ( Sub s onic Jet at High / u . w S p eed Cr u i se) / r 3 557 X S / C VariablePitch l f , 0. 6 0 A B n ( 8 0 0) Narr o wChor d i f __ -5 °

0 . 66

"= . , y, . . - o . s o

. 2688 11_ " 0° O.5 2

( 60 0 ) I / _ ' o .45

X-,_ ------16 ° 0.78 (200) S / C - C / C N a rr o w Ch o r d X -_ -----+ 4 0 0 (Supe r son i c J et at H i g h Speed Cr u i se) 0 I | • _. I ' ( ) 00 2000 " 30, 'v _" ,_ P r o p elle r Spe e d rp n 1 ( b ) L o w Spe e d Cr u i s e :38.1 m / sec , a t Se a leve l ,(1 2 5 f t / s e c) Fi g ur e5 , P r opel l e r Ope r a tingCh a r ac teri s tic s

2 5

V J ; ) . @ With t h i s p ropel l e r effici e ncy assu med,t h e thru s t av ai la b le with th e e ngin e op e rating at f u ll throttlewa s calc u lat e dand plottedagain s t rpm a s the d as h ed lin e i n F i gu re 5 a . E a c h p r o pelleri s c apable o f , pr ov i d i ng t h e thr us tre qu ire d at a b ou t the maxim u mh o r s e po wer av a il a ble fr o m the s electe d air p l a n eengi n e at cr u i s e rpm. Bl o wingc on tr o lcan be us e d f o r s te a d y- s tate hlgh- sp ee d flight at a c o n s t a n tengine rpm t o acco mm oda t e so me d e c re as ei n airpl a n e wei gh t be l o w t he des i gn wei gh t ( sho w nas _i n F ig u re5a, t o W = 1 333k g , 3000 Ib s ). A f u rtherre du cti o n i n weig h t, o f c ou r s e,will re qu irere du ce d engi n e rpm. In c on tra s t, a varla b le- pl tch pr o pellerca n o pewatet h r ou g h a wi d e range o f weig h t a t a c ons ta n te n gi n e s pee d .

Fo r th e s e lec te dl ow- s pee d c o n d iti o n,the thrustavailab l e with the S / C - C / C pr o peller d e s ig n e d with a su b so nicjet at the high- s pee d cond itionIs p l o tt ed a g ai ns trpm i n F i gu re 5 b as t h e s o li d li ne . T he _: pr o peller efficiencyat the rpm at which t h e re qu ire ds tea d y-state " t hr us t i s o b ta ine d(180 0 rpm) a nd the p r op eller e fficiencyat the maxim u mrpm o f 2700 rpm are in d icate d at the en ds o f the c u rve a s 0.7 8 an d 0.55 , r espe cti ve ly. The dashedl i n e s sho w the t h ru s tavailable wlt h _ the engi n e o peratingat f u ll thr o ttlepl o ttedagain s trpm f o r vari ous assu me dv a lu e s of p r o pel l er effi c ie nc y fr o m 0 . 65 t o 0.45. i f It is fir s t se en t h at m o re t h an su ffici e nt engi n e po w e r i s j l avail ab l e f o r stead y- stat e c rui s eat the t h r ust -r equ ire d rpm of 180 0 ; ) • i .e. ,t he S I C - C l C pr op e ll er e f f i cie ncy Is greatert ha n t ha t n e c essa r y I , (<0 . 55) f o r t he eng i ne at f ull thr o ttle to pr o vi d e t h e r equi red thr us t i I fo r st ea d y - state f l i gh t . The eng i ne, t he r e f o r e, would be ope r ated at , ) , r educed th ro ttle f o r st e ad y - state c r u i se a t th i s l ow speed. A m a r g in i s j i th e n av a ila b le f o r climb o r accele r a ti o n .

2 6 _ -• , !

f T h e m axi mumra t e o f cli m b at constant s _ eed is d ir e ctly .J

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pr o p o rtional t o the dif fer encein th rus tavailableat the m a x im u mengine i p o wer o r the ma x imu m thrusta v ailablefrom the p ro p eller fr om that !

- re qu ire d f o r steady-state flight. Fr om F ig u re 5 b, it is seen that the S / C - C / C p r op el le r effi c i e ncyis hi g h e noug h (0.55) at th e ma ximumrpm 1 o f 27 00 t o ab s orbthe maxim um engin e p ower at that r p m. T he thr us t I marginf o r climb o r acceleration which resultsis 1779N (400 Ibs). ( T he thr us t p r odu ce d with the S I C p _ u pell e r operatingas a variable I p it chp r o p ell erat 2 700 rpm for v ari ous cha n gesi n h u b bla d eang le , I a r e i nd icated" x " a t _ o the c o rresp o n d ing prope l ler efficie nc les are ) li s te d . The maximumthr us tavailable with a fixe d -pitch propeller I ( AB = O ) i s le ss than t h at obtainable with the S / C -C / C propeller. The !

t h rust i s limite d by bla d e stall an d n o t by engine p o wer availabilit y as indicated b y c o m p ari so n o f t he FP pr o peller e fficiency(0.52)with the full-thr o ttle t h r us t-available c u rves. Th e V P propeller with a hub ,_- bla d e angle change o f -5 0 pr od uces the largest excess thr us t. Fo r this case also, the enginewould be operatedat part throttle, whereasthe S I C - C l C pr o peller operatesat full throttlebecauseof a lower - :c - efficiency (0.55 v s 0. 66 ). '-e_ o T h e r esul ts s h o wn i n T abl e 5 i nd icatet h at, t o match the re q uired thru s t f o r ste a dy-state cruisewith a fixed pitchnarrow chord propeller i

l

at the se l ec t ed l o w s p eed , a n en gine rpm o f 2 1 00 i s re q uired. Although I the analy s l_wa s done at an rpm of 2700 for the VP propeller,it I s !

) cle ar fr o m F ig u r e 5b that th e VP p r o pell e rca n be adjustedt o op erateat I a n y preferredrpm. !

A l so pl o tt e d o n F i gu r e5 b ar e r esu lt s f o r a S / C - C / C p r ope ll e r ,1 with a n a rr o w c h o r d simi l art o the S / C FP a nd V P p r op el l erch o rds. T he j !

. _ 2 7

\

""q , 2 1 . , • : _ - _ _ * ' , " "' '_" , ' , ,- ........ i_ _ C / C p r ope ll e r wtt h na rr o w chord w , _ s u nab le t o ach t eve t h e r equ t red l o w -sp e ed stead y -state f l tgh t t h ru st a t an y eng i ne speed because of b l ade s tall at ang l es o f a tt ack l ess t han t ha t f o r s tall o f t he th t n t ra tl tng edge S I C a trfot l . Even t f somechange tn des t gn cou l d permi t ach i evement of t he re qu ir ed t hrus t (a t ab o ut 2100 r p m ), no excess th ru s t for c l imb o r acce l e r a ti on w ou l d ex i s% 3 . 4 Ope r a ti ng Bounda r ies The ae ro d y na m ic data used ( r eference 3) w e re me asu r ed ove r a 11mtt ed Re y no l ds numbe ra nd M achnumbe r r ange. Fo r t hts s t u dy , t he Cd,C L and c _ vs _ rel a ti onships w e r e assumed t o b e t nva r tan t . Ex tr apo l a t ion o f the expe r i me n tal da t a ove r a r an g e o f nega t tve ang l e of a tt ack w as r equ tr ed fo r a po rtt on of t he s t ud y . Ope rati ng bounda rie s t h a t shou l d b e obse r ved a re ill us tr a t ed t n F i gu r e 6 and d i scussed as f o ll o w s.

+ 3.4.1 Use of Positi ve l t ft Coeff i c i en t I t ts poss i bl e t o ope r ate ove r a small r ange of nega ti ve cjL f o r t he i avotded to prevent loss of prope ll er effect i veness tn event the b l o w tng ' L ts d i srupted by equ i p me n t malfunct i on.

; S I C - C / C ai r fotls and secure p os iti ve c t _ b y blo wi ng. Th i s should b e !J_!

3.4.2 Use o f Lo wAn g l e of Attack I On the b l o w n at r fo t l, the degree of contro l of c L w tt h c h ang e s tn ( I the momentu m coefficient va rt es wt de ly w i t h ang le of attack. Fo r I exa m ple, a t zero deg r ees angle-of-at t ack, a change of c _ f r om 0 t o .01 i i produces a change t n c L from 0.38 to 0.90, a rat t o of 2.37:1 Inc re ase. t i : : i A t an ang l e of a ttack of +9 , fo r the samec _ change, the c t va rt es from i t 1.16 to 1.48, a r atto of 1.28:1 T M s ts almost a 2:1 change tn '; I * ] 1 , I effec t ive cont ro l b y b lo w tng. Becauseof t he dest r e to w o r k a t l o w t o " a ngles, t t w as necessar y to p rovtde w tde chords to p r ovtde the r equt r ed _i t

ORIGINA L PAGE181

OF . P OO R QUALrr Y C . = 0 . 0 5

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Q • t • . _ 0 " 1.( ' _ '

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t L - _ -= 30 O pe rating Ar e a 0. 5 i r NASA 17 Percent ' I

I c Supercritical Airfoil

( R N ) = 2 x 10 6

C d , , -0 . 02 - 0 . 01 0 ]0 . 01 0 . 02 0.03 0 . 04 !

Cd f

N ega tiv e c _o " - Sd ec _

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F ig u re 6, Drag Po lar s f o r S / C an d S / C-c / c Airfoils ( c o nfl , quration 5 o f ref 3 ) i with P r ope ll e r O pe rating Boundaries i 29 _ thr us ts. As sho wn a bove (3.3.3 , ) on ly t he w i d e chord C / C p r opel l ers p r ov i de r e a sonab l e pe rf o rm a nce.

3. 4 .3 Avo i d a nce o f Supe r sonic J e t Ve l oc tty Fo r t he ai r p l a ne a nd p r opel ler s s t ud i ed, propel l e r t ip ve l oc iti es w e r e subsonic, a nd it w a s poss i b l e t o des i gn propelle r s wit h c ir cul ati on con tr ol out t o t he t ip. A lt hough somecompu tati ons w e r e m a de w h i ch r esu l ted i n su p e r son i c j e t ve l oc iti es (e.g., r esu l ts presented in F i gu r e 5b ), ther e are n o da ta reg a rd i ng t he aero d ynamic per f o rm a nc e wi t h hi g h j et ve l oc i t i es. To keep t he j e t ve l oc iti es subson i c , t he m omentu m coeff i c i en t s h a d t o rang e from no m o re t han 0.002 a t the ti p t o 0 . 004 i nboard . The approx i mate boundar y for s oni c m o m e mt u m coeff i c i ent i s shown i n F i gu r e 6 f_r t he s in g l e - p l enum p r ope ll er.

3.4.4 S ec ti on E ffi c i enc y T h e c £ / c d pl o t i nd i ca t es t h at m a x i mu m L / D i s se c u re d fo r th e S / C : ; a ir fo il a t ang l e o f attack o f about 5 ° , and f o r the S / C - C / C a t abou t 4 °. The L / D does no t li near l y a ffe c t prope ll e r per f o rma nce as it does f o r wings on aircraft. In f act , u ntil the L / D de cr eases t o abou t 3 0 , I t he r ea r e onl y sm all e ff ec t so n p r ope ll e r p erf o rma nc e. Th e L / D f o r t h e "__ t r ,I f ' _ _ $ / C - C / Cis a bove3 0 f o r a n g l es - o f- a ttack do wn t o ze r o de gree s . Lo w e r

i

!

: I a n§l es will h ave s ig n ificant a dve r see ff e ct son p r ope ll e r p erf o rm a n ce , i , I ( M omen t um coe ffi c i e nt s be l o w 0. 02 a re des ir ed , (se c. 3 . 3.1), t o t / _ p r even t ex c ess i v e de teri o rati on o f s e c ti one ffi c i en cy. I n gene r a l,t he i superson i c J e t b ounda ryr es trict s o per a ti o nt o be lo wcp = 0 .0 05; jl ho w eve r , wit h m ul ti- p l e n u m s yst e m s, it shou l d be poss i b l e t o ope r a t e !

' w i t h so mew h at h i gh erm o me n t u m coef fici e nt s t ha n 0.005 nea r t he hub a s a , ) J ,J me ans to i mp r ovep r ope ll e r pe rf o rm a n c e, i q

l

I 3 o

r '

3.5 SystemDesign C o nsiderati o ns In this limitedstudy,only aerodynamic performance was computed and analyzed. Other designconsiderations such as noise, structural . analysisand design,systemweight,ductingand seal design,and type of compressor were considered but not in enoughdepth to warrantmany conclusions; however,no largetechnicalproblemswere apparent.

Becauseof the small slot size,it is judged that the noiseenergy would be locatedat high frequency and thereforenot be a problem.

Also, bl o wingi s on ly us ed for the high-altitude high-speed c o nditi o n i and not at low altitudes. The structuralproblemswere only examinedto the extent that it appearsreasonable to make the trailingedge assembly as a sub-assembly of the main propeller blade. The small size and dimensionsof the slot lead to concernsregarding nicks,distortionand structuralfailureunderc o ncentrated l o ads. The design o f pneumatic _ ' shaft seals is believedto be straightforward.

The compressor requirements to compressthe ambientair to the hub pressuresrequiredf o r a typicalpr o pellerare listed o n Table 6. While _s_ the c o m p ressi o n rati o is higherthan that requiredf o r supercharging the _"_ airplaneengine,the mass fl o w is smalland the c o mpressi o n h o rsep o wer o nly ab o ut o ne f o urth o f that requiredf o r the engine al o ne. Valving o f the chargeroutputswould be suitableto controlthe hub pressure. If t he airplane e n g i n e i s no t s uper c harged, it is p o ssiblet o o peratean j a u t omo tive type p os itive d isplacement unit (vane o r R oo ts type)as a !

I I b e lt- d riven a c c esso ry. The _r u ise intakeair pumpingrequirement is i 0.92 liters( 5 6 in 3) per crankshaftrev o luti o n and is c o mparablet o the ,4 pump in gvo l u m e ratesa v ailabl e fr o m the aut o m o tive market.

t i

: : " i}

_ j Tabl e 6. Air Fl o w R e q uir e ment s F o r a S / C-C / C ._i Propeller Driven by a Supercharged Engine .

_p "_'. Propeller* Engine Total .? Air Flow Required 0.038 kg / sec 0.0159 kg / sec. 0.097 kg / sec "_ _ (0.0026 sl / sec) (0.0310 sl / sec) (D.0336 sl / sec) :: C om p r e s s ion Ratio 1.22 1.078 - -_ Compressor Horse- 1.214 5.02 6.23 po w e r Re qu ired , C o m p re sso r H o r s e- _" power Available 18.2 N o t e: Op e rating con d itions for 3.06 km,(lO,O00 ft), at 2500 rpm with "- a Tu rb o charged e n g ine o f 8 .52 liters, (520 inJ), _- displacement, (ref 2) _ * Th e propeller r equ irements include an allowance for leakage and __ losses within the ducting.

°" i

I

f , io

t

- } E I II _ 4. 0 C O N C L U _IN_ REMAR KS ;I A spe cia ll y- de ve lo ped co mp ut er p r o gram ( pre s ented in t he Appe nd i x) I has been used to comparethe aerodynamic performance of propellers. The comparisons were made for a 1600 kg ( 3 600lb) _!i I circulation-control ( C / C ) pr o pe ll ers with variable-pitch and fixed-pitch single-engine generalaviationairplanewith a maximumspeedof about The stu d yindicated that, on an aerodynamic performance basis, the !l 3 00 km / hr ( 186miles / hr),the approximate limit for a fixed-pitch propel l er.

circulation-control propelleris feasib l e. Increasedspeeddecreases • _ the potential feasibility. Inability to featherand reversethrust limitsapplicability to single-engineairplanesor multi-engine configurations where engine failurescan not producea disturbingtorque (e.g.on-axisconfigurations).Economicfeasibility requiresanalysis _i of manufacturing and maintenance costs of C / C propellers as well as

l

appraisal of m i ssionrequirements for specificairplaneapplications.

r All of the propellers investigated had approximately the same efficiency at the high- s peed crui s e designcondition. At low- s peed, the C / C propeller performance (cruise,rate of climb,and acceleration) was bettert h a n that of an unblownfixed-pitch propeller but not as good as that of a variable-pitch propeller. Althoughblowingat high-speed permitsoperation througha wider rangeof angleof attack than for an unblownfixed-pitch prope l ler,performance is con s trained by the amount of blowingpermi s sible.The amount of blowingis limitedby decrea s e s • maintaint he bl o w n jet velocityto subsonicvalues. The latter I in e fficiency with in c rea s e s in blowingpowerand by the de s ireto , 33 ' I Z_ c ons tra i nt wa s i mposed i n the i n terestof c ons ervatism b ec a us e no , _ experimental data are available with supersonic jet velocitie s . It . , a p pearedre as onab l e t o expect that the aerodynamic effectivene ss of the , C'I _ -- ' I C oand, j e tw ouldde t e ri o rat e wit h s upe r son i cb l o wi n g . Im p r o ve d . _ !/!il _ perf o rmance, however,appear s po ss iblethroughcompartmentation of the __ b l o wi n g p le nu m a lc n _ t h e p r ope ller sp a n t o p r ov idei n cre a s e d subson ic _!

. b l o wing a t t h e l o wer-speedin bo ar ds ecti o ns. The flexibility of _; , I) t_ _ , op eration f o r a v ar!_ble-_i_ch p r op e lle r will l i k elyyield su peri o r I , .

_ p erf o rmanc e a t all off- d e s ignl o w- speed c o n d itions. T he poss i b l e _ ov er a ll a dv a n ta g e s o f C / C p r o pellers, therefore, depen d u p o n e c ono mic i_i .T c o m pa ri sons , i _ , A l i m itedap p raisal o f o ther than aero d ynamic design i c ons id e ration s , such as n o i s e, str u cture, w e ight,ductlng,and s eals, ), .

_/i ] indicated no largetechnicalproblem s for C / C propellers. The , -_ co m p re sso r re qu irements can be met with autom o tive-type compressors or , • by a s mall am ou ntof valve-controlled bleed from an engine supercharger.

C

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_._ _PP EN DIX

o / .

: ,_ ., _. A BA S I C CO MP UT E R PROGRA M FOR THE AERO D YNA MI C

'_' D ES I 6N OF A I RCRAFTPROPELLERS AS F I XE D P I TCH, VAR I A B LE

" P ITC H OR C I RCULAT I ONCONTROLLED ,

: By W a y n eH. Brya n t

NASA Langley Research Center

: _i . l I n t r odu c ti on 3 6

,_. General De sc ripti on o f Maj o rPr o gram Sec ti on s 37

'-; C a s eTableIde n tifi c ation f o r t h e Prese n t Stu d y 43

-_. :

P r og ram V ariable Defi n iti o ns a n d Pr o gram Listing 45

P r og ram L i s ting a nd Cros s References 51

S ymb ol Cr oss Ref e renc e T ab l e 70

e"

_. Detai lP r og r a m Descri p tl on 78

Rep l aceme n t Co d ef o r Partial SpanBlowin_ 82

Sugges ti ons f o r Tailoring Pr og ram 85

Con c lud i ngR emar ks 87

i A PPE NDIX

by

W a y n e H . B ry a nt N A SA La ng l ey R es e arc h Cen t e r Introduction i i This appendix de sc ribe s t he co mpu t er pr og ram devel o ped t o g enerate the da t a i n the presen t s t udy. Thi s a ero dyna m ic pr o peller desi g n pr ogr_ n can acc o mm o da te mi nim u m l os s ( ref. 4) fixed- or varia b le-pi t ch pr o pel l ers, and c i rcu l a t i o n- co n t r oll ed pr o pellers wi t h a sin gl e plen u m ex t end i n g fr o m the r oot t c an y g iven radiu s . The pr ogram was i m p l e me n t ed in B A SIC s o t hat o n ly a m l n _ m a l c om p u ter investmen t is re q uired t o u s e i t to desi g n p rope l l er s . T he presen t w o rk was acc om p l ished u s in g a D ig ita l Eq u ipmen t C or p or at io n V A X-I I/ 7 8 0 s uperminic o mpu t er, and t he BA SIC l an g ua g e e lem en t s c o nf o rm to t h o se u sed in VAX B A SIC . A n effor t was m ade t o develop as m u c h of t he pro g r am as po ss i b l e i n " s t andard " B A SIC t o ea s e its t ransi t i on, to ot her ma ch i ne s . T o t e s t t h i s, the pr og r am was t ransferred to a CDC Cy be r 1 7 5 c o mputer a t LaRC where appr o x i ma t e l y t w o h o urs were re q uir e d to ob ta i n s ucces s ful o perati o n. C o mm en ts o n pr ob a bl e c o d i n g chan g es required / desired ap pe ar a t t he end o f t h is appendix.

The resu l t s o b t ained u si n g the c o mpu t er pr og ram described here have be en exam i ned and ap pe ar r eas o n a b l e. W hile there are n o kn o wn pr o b l ems o r " bu gs" r e mai n i n g in t h i s pr og r s m, t h ere ma y y e t be pr ob lems tha t will s urface f o r new inpu t ca s es. A dd i t io nal l y, t h e pr o g r am ma kes n o s t ruc t ura l ana l y s i s o f t he d e si gned pr o pellers; th e s t ruc t ural in t e g rity m u s t be ascer t ain e d by th e r _ p r ope ller b uilder u s i n g s o me ot her t e ch nique. _% Th is appendix i s o r g anized in to s even mai n s e ctio ns. Th ese are: Intro duction General Descript ion of Majo r Pro g r am Sec t ion s I m Ca s e Table Iden t if i cat i on for t he Presen t S t u dy I Pro g r am Var l able De f i ni tio n s and P ro g r am L istl n 8 J Det ailed Pro g r am De scr i p ti on ( k e y ed to li sti n g line number s ) i !

S u gg e sti on s f o r T a i lor i n g Pro g ram !

Concludin g Re ma rks t E

3 6

GeneraI Description of Major Program Sections The purpose here i s to gi v e a brief description of each major _ rea encoun t ered in t he progr am . Th i s will b e done firs t in t he order t he sec ti ons are found in the l i s ti n g it self w i thou t re g ard t o ti l e program execu t ion f l ow.

Nex t, a specific case will be given t o i llus t ra t e typ i cal program flow, and appears i n t he De t a i led Pr o gram Descrip tio n s ect io n, i The r e are ei g h t main pro g r am sec t i o ns z _i (i) Case selec tio n (2) Minim m n i nduced l o ss pr o peller desi g n (anal y ti c) a 1_ d o utput i (3) Strip i n t e g ra t ion pr o peller des i gn (Part I), b ot h non - b lo wn and b lo wn ( ci rcu l ation co n trol led) !

(4) Induced vel o ci t y i t erat i ve calc u la t ions (5) Str i p inte g ra t i o n pr o peller d e s i gn (c o mple t i o n) i ncludin g t hrus t ma t ch i n g i tera t ive calcula ti on s _ ( 6 ) Mi s c e ll ane o us calculati o ns (e. g . , effic i ency , Ma th n u m b er , e t c.)

( 7 ) Line print e r and cross plot file o utput '_ (8) Subr o utines The main pur po se of each sec ti on is g iven in t he t ex t t hat follows. The l i ne n um bers list ed correspond t o t he pro g r am li s t in g found l a t er i n t h i s append i x.

Whi le t h i s pro gram was devel o ped t o g enera t e data f o r t he s t udy presen t ed i n t he ma in bo d y o f t h i s paper, it should be reme m bered t hat rela ti v e l y s_ mple mo d i fic atio n s to the lis t ed pro g ram render i t useful for evalua t in g a varie ty ,_ of propeller de sig ns. T h e data con t ained in t he pro g r am , and t he l o gic s t a t e - : _ meri ts c o n trol l i n g t he p rog r am fl o w, are th o se used f o r t he l as t part o f t he st ud y .

(1) Case Selec t ion Af t er t he array declara ti ons and open i n g ou t pu t fi l es, t he f i rs t par t of t he pro g r am cons i s t s of in it ializ i n g var i ables for a spe c i f ic run. Th i s occurs be t ween l i nes 1 7 0 and 1820. A n umbe r of DAT A st ate m en t s contain informa ti on • for t he blo wn propeller lift and dra g coeffic i en t lookup t able as well as t ha t for t en pre-def i ned evalua ti on cases. These DATA en tri es are i den ti f i ed i n t he De t ail e d Pro gr am Descr i p ti on sec t ion follow i n g t he pro g ram li st in g and cross Reference t able. Table A1 i n t he nex t par t of t h is ap pe nd i x s how s t he ma i n ,_

3 7

L l I : i Ji charac t er i s ti cs o f th ese pre-de ft ned cases. If a run i s desired f o r wh ic h no i case ex it s , all requ i red da t a c a n be man u ally en t ered from t he keyboard durin g !

"I program exe c ution. A l l pr ope l ler desi g n s u si *, ma nually e n t ered da t a will be _ ev a luated as " on design po i n t" c ases l t ha t i_ , t he pro pel ler's pe r f ormance i n i some arb it rary o ff -de s i g n po i n t canno t be ma de. The " o ff -des ig n po i nt " ev a l- !

1 ua ti on f ea t ure is b ui l t i n w it h t he use o f p r e -de fi ned cases.

The engineering un it s f or each inpu t parame t er i s di s played a : t he value ':I i s reques t ed. Th e s e s _m e un it s are used f or pre-load i n g t h e de f i ned oases i n t he d at a s t a t emen t s. The da t a order f or t he de f ined oases will be given in more de t a i l la t e r . In a d d it ion t o d at a f or t he ac t ual pro pe ll e r des i gn, t he program' I nqu i res whe t her e it her o f t wo f orms o f d i a g on i s ti c ou t pu t is required f or t he curren t r u n ( bot h predef i ned or man u al i npu t cases). The firs t s e t _i of o u t pu t i s rou t ed t o t he prin t er and i s use f ul for observing t he c onvet' g en o e du ri n g induced velo cit y and t hrus t ma t ching iter a ti ons _ t he second s e t rou t e s d t he i n f lo w it era ti on da t a t o t he console d i splay device (CRT) so t ha t t he user can observe convergence in real- t i me .

_ (2) M i n im um i nduced l oss pro pe l l er design and ou t pu t (Analy t ic) _ Th e nex t sec t ion designs a non-blown pro pel ler a t t he given o pe ra ti ng -: _ c o ndition _ s l ng t he t e c hnique de s cribed by Larrabee in reference _ . This sec tio n i s based al m o s t en t ire l y o n a propeller d e si g n pr og ra m deve lo ped by W . He _itt Ph i ll i p s and E. E u g ene La rr a be e for an H P 983 0 , _ e skt op co m p u ter .

The c o de im p l e m en t ed ra nK es fro m li ne 182 0 to li ne 3 860 _ e q u a tio ns n ot ed i n t he R E Ma r k st a t emen ts refer t o t he n umbe red equa t ions of (ref. 6), and are _ . all con t a i ned i n t he li st in _ _ .' t hin ankle bracke t s (e.g. _ E_ N 21 _ ). _ A f t er loadin g da t a r e quired f o r t he non-blown pr o pe ller t able look-up s ubrou ti ne, t h is s ec ti on ob t a i ns t he l if t and dr a g coef f ic i en t s for _ he a nkle i of a tta ck s panwise d i s t r i bu t i o n prev i ously en t ered. Th i s is accompli s hed i t hrough a s ubrou ti ne call t o t he non-blown pro pe ller l i f t / drag subrou t i n e. } Aft e r t h _ se qu an t i t ie s are calcula t ed, t his se c t ion de t e rm ine s t he s pa nwise i chord d i s t ribu t ion, efficiency, required ho rs e po wer and t orque , t he local !

Mach and Reynolds n um ber s, an_ other pert i nan _ dat a. The se data a re t he n i out p ut to the li ne pri u t e r file. i At t he en a of this section , chord and be ta s pan wise d i stribu _i ons a re J sav _ f o r la ter predefined case analy s is. A more comple t e descrip ti on of t h i s , _ i me c h an im is Kiven i n t he detai led progra m descr ipt ion.

, 38

, t P" _

q " !

( 3) St r i p i n t e grati o n propeller des ig n (Part I) This sec ti o n is c o d e d in lines 38 70 through 4590 and implem e nts e quati o ns found in t he m ain body of this report. Th ese referen c es are denoted within the REMark s t atements using square brackets (e.g. [EQN. 7] at line 3 900). The strip integrati o n secti o n can design eith e r blown or non-blown minimum induced- l o ss propell e rs ; this feature is controlled by the d e signer at program se t up tim e .

Th e str i p integr a t i on d e s i gns w e re c h ec k e d a g ai nst th e a n a lyti c d e signs a nd g a v e r e sults i d enti ca l within a few per ce nt a lthough th e r e w e re sm a ll cha ng es i n t he s p a n w ise c hord an d an gl e of attac k di st ribution. Th ese c h an g e s L in a ngl e o _ a tt ac k result in a n in c re a sed t h rust whi c h is c omp e n s at e d for (in t a late r prog r am s ec tion) by s c aling th e spanwis e c hords to ach i e v e the | re q u i r ed t h rust. Co m p ar iso n o f t he o u tput f rom t he ( n o n- b l own) ana lyti c des ig n i w i th t ha t of t h e (non-blown) strip integr a tion d e s i gn shows sm a ll c hanges in the sp a nwis e c hord a n d a ngle of a tt ac k distributions.

(4 ) In duc e d vel o c ity i teration ca l cula tio n s This s ec tion implements t h e iter a tive e qu a tions ne c essary to det e rmine t h e tru e sp a nwise bl a d e a ngl e of att ac k w h i ch is different from th e nomin a l be ca use of indu c ed velo c ity. Lines 4600 through 5420 realize this pro c edure. The te c hnique used here is derived from (Ref. 5) and is listed here in full for c onvenien c e. Referen c es to equations i n the c omment portion of the individual s tate m ents or i n R EM a rk s t a teme n t s a re en c lo s ed in s q u a re br ac kets ar id hav e a n !

"A" ( f or appendix) prefix. For example, li n e 4 7 10 has a comment ( t he text following the "!") indi c ating that line i m plements equation AI ([EQN. All); that equa t ion itself follows.

The indu c ed velo c ity co mpon c nts are ev a l uate d at e ac h ra di a l blad e s tat i o n, i, by th e it e rative pro c edure listed b e low. To st a rt the iter a tions • is used t o f i nd t he ini t i a l estim a t e of _i a s a i " 8i " _i (A 2 ) Th e pro ce dure c ontinu e s by finding th e multipli e r 4

i

!

39 _

J ORIGINAL PAG E |_ ' ; OF POOR QUALr P_ . . _ B ci - - Ki . -_ C A3 ) T c ° s'l " -}2 _ whi c h i s t hen us ed i n the ca lcul at i o n o £

Ki ( cc o s *i) ) (A4)

a. = _ s in2 0i "i -2 z (I Z 1 / C t i(c° s _i) )

_i n * i i

a nd / = _ o s ¢i (AS) a i (l + li l Cti os ¢i Th e induced vel c _:ity C _l_nents ai a nd a _'z a re next used to ca l c ul a te a n

upd a ted ¢ as

_C l - • * 1 a' i I = , t a n_l( + 1 + ai ) (A6} which i s u s ed in o b ta ining a c o rre c ted a in = a i + _(¢i " ¢ c ) ( A 7) _, " -_,, a c i i i The c o rr ec ted a n gle - of , at t ac k i s used t o c al cul a t e a co rrec t ed _ a s i

I

= (AS)

¢ci L _i a ci ] which i s used if f u rth e r i t erations ar e neces s ary.

Th e co n v er g en c e tes t s co usi s t s of co; d_ p arin g t he curr e nt i te r at i o n value of I a c . wi t h th e pre v io u s i t e r at ion v a l u eo f a i at e ach blad e stat ion a n d d ec l a ri n g a J c o _ ve r go d so l u t i o n if t he absolut e differ e n ce at e ve r )" blade station is less than i t ha t of O.OS ° . S tated m at h e ma t i c ally , t h e test i s , !

( a i - a c.) < O .OS ° F o r a l l b lade sta t io n s , i. ( Ag) .I

t

If any st a t ion fails to m ee t th i s cr it er i a, t he procedure it e r a t e s s t ar t - i n g wi t h E quati o n A 3 j if the c o rrec t ed ang l e- o f-a tt ack a t all b l ade s tat i o n s pa s s t he t e st , p ro g ra m fl o w is to t he sec o nd par t o f t he st r i p i n t egra t i o n desi g n. In ei t her case, new l if t and dra g c o efficients, ba s ed o n t h e mo s t • . recen t ly correc t ed angle- o f-a tt ack , are calculated for b ot h blown and non-blown de s i g ns a s appropri a t e.

I : _i (5) S t r i p In t e g r at ion pr o peller des ig n (c o mpleti o n), and t h rus t m a t ch i ng sec t ion i s coded be tw een l i nes 5 4 30 and 652 0 , w it h t he t hr u s t mat ch- / .

'- i ng par t be t ween 566 0 and 651 0 . Af t er t he i ni t ia l induced ve lo c it y c o rrecti o ns are ma de t o each blade s t a ti on's a ng le o f at t ack, t he differential t hrust and to rque are de t ermined. The t ot a l thr u s t is o b t a i ned by n um erica l in t e g rat io n a nd is c om pared t o the required t hrus t f o r the indica t ed fli g h t c o nd itio n. If !

_ - , t he devel o ped t hrus t d o es no t mat ch t he req u i red thru st w i th i n 1%, t hen so m e _" fo rm o f ad j ustmen t i s empl oy ed. Th i s is acc o mplis h ed i n an it era ti ve fashi o n , wi t h t he a djus t men t parame t er se l ec t e d by a comb i na tio n of cas e i den ti fica t i o n and con t r o l var i ables. After t he ad j us t men t has been made , pr og r am fl o w re t urns to t he i nduced vel o c it y i t era tio ns to acc o un t f o r t he presen t t hrus t _ _ . mat ching cha ng es. Th i s sequence is repea t ed u n t il t h e develo pe d t h ru s t is ©., wi t h i n limi t s indicated ab o ve , or t he de sig ner ma nually t erm i na t es t he run.

. This pro gram sec t i o n la rg ly con t r o ls the manner i n wh i ch cases are in t e r- pre t ed , i.e. , t he sequence i n which cases must be run t o o b t ain m ean i n g ful ° resul t s. ( Thi s sequence is discussed in t he de t a il e d e x m _ ina t i o n of t he lis t- Z " in g .) F or t h e cur r e nt pro g ram, a lp ha , be t a, eng i ne s p eed, or t he pr ope ller ch o rd is sca l ed o b t a i nin g desir e d t hrus t acc o rd i n g to cas e u nder evalua tio n.

T o m o dify t he p rog ra m f o r o n e ' s pa rt icu l a r n e eds, a goo d u nders t andin g o f t h i s s ec t i o n is required , since mo s t chan g es wi ll be made here.

( 6 ) Ni sce ll ane o us c a lcu l a tio ns This s ec ti on s t ar t s a t line 6530 and en d s a t line 7290. D i fferen ti al t orque is n um erically in t egrated to o b t ain tot al t orque. If t he de sig ned 'i pro pe ller uses C oa nda blowin g, t hen t h e tot al a i r mass fl o w, and t he • cen t rifu g al and compress o r en g ine h o rsep o wer for t his air flow are ob t ained.

'I " Nex t, aer o dyn am ic to rque i s c o nver t ed to horsep o wer using I

-1 41

, !

and t he t o t al useful wo r k (in h orsep o wer) is ca l cu l a t ed. From t h i s da t a, p r o pe l l e r eff i c i enc y is then ca lc u l a t ed. Fi nal ly , a t each bl ade s t a tio n ; ( a ) lo cal Mach n u mber a s Vi

_)i = T s Cili)

w it h V s = ve l oc i ty of sounda t curren t a ltit ude, (b) Re ynold's numbe r (I_3 i = P® CiVi CA12) w i t h p_ = a i r de ns it y an d p. = v i sc o si ty and (c) t h e D r ag/Li f t ra t io

%i C A in) , - _

l a r e calcula t ed .

The sec tio n ends wit h t he de t er m in a tio n o f t he ava i la ble h or s epo w er a t t h e .- _ - , Y cu r r e n t engi n e spe e d fo r t h e a i rcraf t selected i n t his s t udy, and t h e possi bl e : . _ , ra t e-of-cl imb fo r t h e pr o p e lle r / eng i ne / a i rcraf t sys t em. [ J (7) Li ne prin t e r and cr o ss-p lo t fi l e ou t pu t Th e n e x t pr og ram s e c tio n r uns f rom l i ne 7300 to l i ne 8 4 0 0. I f t he case _ .

under e x a mi nat io n ca l ls f or of f - d e s ig n p o in t evalua tio n , t he p rog ram save s _ pe rti n e n t i nf o rma tio n i n a disk f i le for la t e r proc e s s in g . T h e s aved da t a and t h e f i l _ fo r m a t a r e discussed i n t h e de t a il ed p ro g ram descr i p t i o n . Next , L i da _ a f o r t h e app r op ri a t e des i gn t ec h ni q u e is ou t pu t . Thr e e f o rms of pr i n t er i

)

o u t pu t a r e ava i la b le z (a) analy t i c ( n on-bl own ), ( b ) str i p i n t e g r atio n (n o n - i bl own) , and ( e) s trip i nt e gr a t i o n (b l o wn). T he part ic ul ar co m b i na t io n o f !

] o ut put p ri n t e d is d et e r m i ned by case n um b er and con t r o l va ri ab les, I A ft e r th e o utpu t i s c om p l ete , th e f i nal bet a and cho r d values fo r th e !

I des i gn case p rope lle rs a r e saved fo r use i n t he o f f-des ig n ca se eva l ua ti on. I Th i s s ect i o n en _s wi t h a quer y t o e it he r ex ami ne ano t her case o r s t op t he prog r am .

4 2 > (8) Subrou ti nes i The pr o gra m subroutines can be found star ti n g at line n u mber 8 4 10 and runni n g t o t he end o f t he pro g ra m a t li ne 971 0 . Aerodynam i c coe ffi c ie n t s _ for t he non-blown pr o peller ar e o bta i ned from a l o o k up ta b l e s u b r o utine be tween li nes 8 4 10 and 8 7 7 0. A Sim pson ' s R ule i n t e g ra t i o n scheme i s found s t ar ti n g a t l i ne 8 7 80 and e nd i ng a t l i ne 89 2 0. An a t mospher i c character i s ti cs subrou ti ne , reproduc i n g t he values g i ven in t he 1 962 NASA s t andard a t m osphere repor t (Ref. 6 ), i s nex t , runn i ng from li nes 8930 t o 91 9 0.

The Co a nda e f fec t , blo wn t ra i l i ng edge pro pe ller aerodynam i c coe f f i c i en t s s ubr o u t i ne be t ween 9 47 0 and 9630 i s u sed to ca l cu l a t e r a nk i n t erval s f o r t h i s subro u ti ne i s l oca t ed s t ar ti n g a t li ne 9 2 00 and end i ng a t li n e 9 460 . Th e t he ava i lab l e eng i ne h o rsep o wer as a f u nc tio n o f e ng i ne s pe ed a t f u ll t hr ottl e } " I lo o k u p t able. Th e f i nal s u brou ti ne r u n s from 9 640 t o 9 7 1 0 and cal c ula t e s f o r t he e n gi ne u s ed i n t h i s s t u dy.

Case Table Identification for the Present Study The current pro gr am i s s t ruc t u re d t o d e si g n s i x pr o pellers i n cas e s I , 2 , , 3, and 4 . These p rope llers are d en ot ed A , A' , B , C, C ' , and D. Ca s es 5 - I0 are f o r of f-des ig n poi n t eva lu a t i o n. Ta b le A I li s t s the c hara ct er ist i cs and

1 '

c o n t r o l par am e t ers f o r each case. Def i n itio ns of t h e var i a bl es and c o n t r o l pa r am e t e r s l i _te d a t t he b otto m o f each c ol u mn , and i n t h e t ex t t ha t f ollo w s t h e t a b le can be f o u nd i n t he l is t o f sy m b ol s t ha t preceeds the pr og r am l isti n g.

Ta b le AI. P r op eller Des ig n P ro gr am Case Iden t i fi ca tio n E va lu a te (? ) Fix ed Dur i n g Th ru s t C or r e c tio n ( ? ) _ , - Case # Alpha Des ig n B l own / No n-bl o wn Blo w i n g Chord Bet a A l pha RP M J l ( A / A ' ) +4 O n Y (A) / Y (A') O n Y / N Y N / Y Y 2 ( B ) -12 , 5 O n Y ( B ) / N O n Y / - Y N / - Y I 3 +2

(c / c,)

On Y (C) / Y (C ° ) O n Y / N Y N / Y Y I 4 (D) -12 ,5 O n Y ( D) / N O n Y / - Y N / - Y ] ] 5 (A) +4 Off Y(A) / N Off Y / - Y Y / - N , 6 ( B ) -12 , 5 O ff Y ( B ) / N Off Y / - Y Y / - N I ] , . - 7 (C) +2 O ff Y( C ) / N O ff Y / - Y Y / - N f 8 (D) - 12 , 5 Off Y(D) / N O ff Y / - Y Y/ - N 9 (A') +4 Off N / Y(A') - - / Y N - / Y Y , l i

lO (c,) +2 off N / Y(C') - - / Y N - / Y Y .!

T8 A(I,I) * C7 * C5 B7 C6 * Parame t er var i a ti on by case number i den tifi ca ti on i s con t rolled by t he va ri able li st ed a t t he bo tt o m o f each col u mn. For t hose col u mns wi th _ , t he

]

param e t er is em be ded wi t h i n t he pr og ra m it self, and canno t be changed wi t h o u t m o dlfyi _ t he source c o de. The pr o peller iden t ifica tio n f o r t h e te n cases se t up in t he acc o mpanying li st ing are s hown und e r t he " Cas e # " c o l um n i n pa ren t hesis (e. & . ( A / A')).

A n example i s helpful in u nders t and i n g t h i s t ab l e. For Case # 1, (T8=I) t wo pr o pellers are desi g n e d, den ot ed A and A'. Both pr ope llers have a nominal I value of alpha of+ 4 degree s (A(I , I)), and are considered t o be desi g n e d f o r t he o pera t in g cond it i o n s speci f ie d in t he Q(I, _ ) arra y as ind i ca t ed by t he "O n " i I i n t he De si gn co l u mn. Bot h a bl o wn and a n o n-bl own pr opell e r wi ll be eva l u a t ed (C 7 =3) , and f o r t he b lo wn pr opell er , t he t rai l in g edge je t s will be ac t ive ( B lowlng ? ). The p r opeller s are d e s i gned to ma t ch t he available t hr u s t to t he required t hrus t specified in t he Q( I ,3) e l e m en t . This can be d o ne severa l w ays . Th e next f o ur c ol u mn s s pe cif y f o r each pr o pe ll er / case which scheme i s used t o ma L ch t he available thrus t t o t he required t hr u st. F or t he blo wn i pr o p e ll er, t he a l pha v al u ._ ar e s ca l ed to acc om p li sh t he mat ching (as can be seen b y t he N( o ) in t he firs t pa r t o f t he en t ry under " Al pha".) F o r t he n o n- ,J b l own p ropeller, t he chord s are s caled, as can be seen from th e / N (o) under t he " Chord*' c o l u mn. The var i able s C5 , B 7 , and C6 are us e d to s et up t he C ho rd , Be t a , and A lpha col u mns _ and pr o gram l o gic is used t o se t up t he R PM c o l um n, i The predef l ned cases m us t be run i n a spec i fic sequence to ma ke certain t ha t nece ss ary data is available f o r each ca s e. F o r t he curren t p rog ram l o gic, • t he sequences are as f o llow: Case #I Case # 3

/ \ / \

' 4 , C a s e # 2 Case # 9 C ase #4 C a s e # I0

I I '

Ca s e # 5 Case #7

Ca s J # 6 Cas J # 8 '

C ase # 1 d es igns t w o p r o pel le rs, A ' (non-b l o wn) and A (blown) a t t he

,i

de si gn po i n t . A' i s des ig ned f i rs t, and t he chords are sca l ed t o n _ ch

!

t he required t hru st . A i s t hen designed u s in g t he fi na l chord s ob t ained !

fr om propeller A'I t hrus t ma t ch i n g i s achieved by chan g in g t he no m inal angle i th is des ig n are t h ose obt a i ned f rom the A' prop e lle r, a nd thr us t ma tc h i n g is ca r ri e d o u t by changing t he n o minal angl e o f at t ack.

In a s i mi lar ma nner, C a se #3 des i gns two prop e llers , C' ( n o n- b l own ) and I o f a tt ack • Case # 2 d es i gns o ne p r o pell er , B ( blo wn). T h e c ho r d s u sed i n , C (bl o wn) , als o a t t he design p oi n t . Again , C ' i s des ig ned firs t a n d t he ii f i nal ch o rds ob ta i n ed d u r in g th e thr u st m atc hi n g i s us e d at t he d e si g n ch o r d val ue s f o r t he bl o wn pr o peller (C) wi t h n o minal angle o f a tt ack m o difi e d to o bta i n t he r e qu i r ed thrus t . Case # 4 des ig ns th e s i xth pr o p eller , D (bl o wn) I # ._ which uses t he ch o rds f_ o m t he C ' pr o peller , and als o chan g es t he nominal !

I angle o f at t ack to secur e t h e re q u ir e d t hrust . I | _Ig Cas e s # 5 , 6 , 7, an d 8 e v a l ua t e the fo ur bl own p r opeller de s i gn s ( A, B , . C , a n d D) at an off-de s ign point. _ o r the s e case s , t he blowi n g is s hut of f , a n d thru s t ma t ch i n g i s a c hieved b y changi n g e n gi n e speed. C ases # 9 and I0 eva l ua t e the t wo non-blown p ro p eller de s igns (A' and C ') at some off-de s i g n condi t i o n, a n d vary the pro p eller p itch to s ecu r e the req u ired th r us t .

En gineering and Program Variable Definition, and Program Lis ti ng E NGINEER I N G P R OG RA M USA G E _ A ( I, I ) A lpha a t e ac h bla de s t a tion, degr e e s A(2,I) Non-blown p r opeller lookup routi n e inte r val const a nts _i A(3,I ) N on- bl o wn p ro pell er lo o k u p rou t i ne alpha !

: i ncr e m en t , de g rees | • A( 4 , I ) Not u sed & - i A S Ou tp u t f orm a t string -_ I I _i A I Alph a a t each bl a de s t a t i on du rin g m a n u al ! s et u p of sp anw i s e di s trib u t i o n , degree s ' _8 A2 bet a i nc reme n t / iteration du ri ng o ff -desi gn . a n a lysis , deg r ees _g to ta I A 3 T otal beta chang e duri ng off - d es ig n anal y s i s , de g ree s A4 L ogi cal: - I = fo r c e d cas e e nd dur in g o f f- d esign ana lysis A5 Squ ar e of j ft v e l o cit y ( t e mpo ra ry v a ri a b l e) !

A 6 A lp ha i nc rem en t / i t era t i o n dur i n g of f-des ign . !

anal y s is, de g re es .I % 45 _ ........ ,N __ " " _°" _ , _ W __' _ .................... '...... _ - _ - _ "_ = _ "' E NGIN EE RING PROGR A M USAGE _ t o tal A 7 C u m u la t ive al ph a ch an g e d urin g o ff- d esi _ anal y s i s , degrees A 8 L og ical: A vail _ ble t hrus t wit hin 1 % o f required t hru st ( A S= 0 ) _ ot herwise A 8= 1 B B N umb er o f pr o peller blades B $ Ou t put forma t s t rin g variable B_ B (I) Be t a a t each b lade s t a t i o n , de gr e e s T (Ref. 4) B 1 Thrus t coe ff i c ie n _ 2T / p V2 _ R 2 C A B2 Adc ance ra t i o p B3 Power Co eff i c i en _ 2P / pV3R 2 C n B5 Efficiency n B6 B lo wn pr o peller efficiency b 7 L o g i ca l : Be t a fixed? l = y es , 0 =n o (C _ ) i C(I,I) Lif t C o efficien t (Cd) _ C ( 2 , I) Drag C oe ff i cien t c / R . C( 3 , I ) C hor d / s pan rat io C (4 ,I ) Unused C$ O u t put f o rma t s tr in g varia b le * C 1 Te m po rary varia bl e V s C2 V e l o ci t y o f so und ( f / s) a t curren t al t i t u de C5 Case da t a: Ch o rd fixed t h is r u n ? l=yes, 0 =n o C6 Case da t a: M o m e n tum c o efficien t s fixed t h i s r un? l = y es , 0=n o _ C 7 Case da t a: Eva l ua t e whic h p rop e ll ers? O =n o ne , l=n o n- blo wn o n l y, 2 = blo wn o nly , 3= bot h C8 L og ical : Cr o ss pl ot this run ? lf y es , 0=n o C9 Tem po rar y variab l e: maxim u m a l pha , de g rees D D Pr o peller diame t e r , feet D ( I ,I) Un u s ed D(2,I) Unused D ( 3 , I) L ook u p t ab le drag i n t erva l c o effi c ien t s ( c d / c E) D( 4 ,I) Dra g to lif t c o ef= i c e n t ra tio D$ O u t pu t f o rma t s t rin g variable . i D3 T e m por ar y _ a rl able I " o ......................

................................ ' ................ p E NG I N EE RING P R OGR A M U S AGE I _ ( Re f. 4 ) E( I) V o r t ex sheet s pac i n g parame t er _ (Ref. 4) F(I) Rati o o f avera g e vel o c i t y incremen t i n the slipst ream t o t he shee t ve lo ci ty F I Temp or ar y va ri ab l e F O R I $ O utput f o rma t strin g variab l e F O R2$ O utpu t f orm a t strin g variab l e F O R3$ O u t pu t f o rma t s t rin g variab l e F O R 4 $ Outpu t f orm a t s trin g variab l e F O R5$ O u t put f o rma t s trin g variab l e FTEM$ O utput f o rma t s t r i n g va ri a b le G _ (Ref. 4) G(1) C i rcula t i o n distr i bu tio n functi o n Vj _ H( I , I) J e t v e l o ci t y at each b la d e st a tio n , f / s _!

(PT) H(2 , I) Je t pressure at each bl ade s tat io n , P S F V. j _ H(3 _ I) L o cal vel o c it y a t each blade s t a t i o n , f / s T H( 4 , 1) Differential thrust ; als o total thrust, Ibs.

Q H(5 , I) Different i al t or que _ als o tot al t o rque, ft - lbs. _ s i n ¢{ H(6,1) Si n P h i - i _A c os _i H(7 , I ) Co s P hi -i H ( 8 ,I) Mass f lo w / f oo t , s l u gs / sec / f oot o_ HP p c _ H (9 , I ) Hor sep ow e r / f oot P _ H A i r density, slu g s / f ** 3 h H2 Al titude , km _ I P r og ram l oo p c o n trol variable _ maxim u m _ va l ue is n um ber o f b l ade s t a tio ns 18 P r og ram t erminati o n c o n t r o l variable !

J P r og ram l oo p c o ntro l var i ab l e i

!

J ( ) B lo wn p r o pe ll er loo kup t a bl e interval !

llf t and dra g c o efficien t s i K Pr o sr am l oo p c o n trol va ri abl e i K ( I ) Blade s t a tio n radiu s to b lade radiu s ra t i o i I K2 Tempo rary varia b le } , L( I , I) Non- blown p r op el l er t a b] . looku p i n t erval !

i llf t coefficien ts ' : L ( 2 , I) U iL used J i ENGINEERING P R OGR A M U S AGE M Tempor a r y variable : (l_q ) _ M(I) L o cal blade stat i onMach nu m ber M O T ot a l ma s s f lo w , slu g s / sec o nd _ N Tem po rary var i able : N1 En gi ne speed , rev o lu tio ns / sec o nd i n N _ E n gi ne speed chan g e / it era t i o n required to ma t ch required t hru st, rev ol u tio n sls ec o nd N3 C um u l a ti ve en gi ne speed c han g e i n ma t ch i n g t hrus t, rev ol u tio n s/ sec o nd 0 Tem po rary va ri ab l e P Tempo rary variable HP t o ta I P1 l iP; E n gl ne power ! als o , P equ i red po we r Pw P2 S t a ti c Pre s sure , Ibs / f _ ' _ 2 H P3 P£ ( 3. 141 59... ) Q Te mpor a r y va r ia bl e V Q (Case#, O ) Airs pee d, f / s n Q (Case # , l) Engin e s peed , r ev. / sec D Q (Case # ,2) P r opell er diame ter , fee t T Q (Ca s e # ,3) Thrus t , I b s.

h Q (Case # , 4 ) A l t i t ude , fee t B Q (Case # , 5) N um ber o f p r o pe ller b lades HPaval I Q (Ca s e # ,6 ) Eng ine po we r , H P . Q (Ca s e # , 7 ) L og ical s Alpha fixed durin g t hru st mat chin g? "-f , l fy es , O =n o i Q (Case # ,8) L ogi cal s B et a fi x ed d u r i n g t hrus t m atchin g ? i l =yes , 0 =n o " Q(Case# ,9) Lo gical # Momen tum coefficien ts fixed durin g t h r us t ma t chin g? l= y e s , 0 =n e .

Q (Cas e# ,lO) Propelle r t ype se l ec t i o n z l=non-blo w n, 2=b lown _ 3=bo t h I al Q (Case # ,ll) Al pha a t b lade s t a t i on 1, degree s I _ a Q (Case # , 12) Alpha a t blade station 2, deg ree s I !

_2 0 Q(Ca s e # , 30 ) Alpha a t b lade st a ti on 20, de g re es } !

I

48 ' _

ENGI N EER IN G PRO G R AM US A GE Q Q6 Torque , ft- l bs (R N ) _ R( I) Re yn o l ds n u mber at each b l ade stat io n R Te mpo rary vari a bl e R R 6 P ro p e l ler tip r ad iu s , f ee t a i (Eel. 4 ) T (I , I) In d u ced ve lo ci t y e qu a ti o n s p ara m e t er a-i " a _ (Ref. 4 ) T(2 , I) Induced vel o city equati o ns para m et er a'-i _ ,, T(3,I) Induced vel o city e q uat io ns c o rrect e d Phi _i " T( 4, I) Induced vel o c it y equati o n s c o r r e c t ed Alpha _i T( 5 , I ) F ina l Be t a fo r Cas e I , ana ly t i c p ropeller (A') 8i T(6,I) _i na l B e t a for Cas e 2 pr o p e ll er (B) 8_ T ( 7, I ) Fi nal Be t a for Cas e 3 , ana ly t i c p ro p elle r ( C ') 8i T( 8 , I ) Fi nal Be ta for Cas e 4 propel l e r (D) 8_ T(9 ,I ) Fi nal Be ta for Cas e I, blown pro p e ll e r (A) 8i T (IO , I ) F i n al Be t a for Cas e 3 , b l own pro p elle r ( C ) ( C / R ) _ T(II, I ) F in a l Ch o rd r a tio for pr o peller A' (C / R ) _ T( 1 2 , I ) Fi nal C ho r d r a t i o for prope ll er B (C / R) _ T (13 , I ) Fin a l Ch ord r a t io f or p ro p el l er C ' ( C / R ) 4 T(14, I ) Fi nal Cho r d r a t io f or p r op eller D _ , ' (C / R) 4 T ( 1 5 , I) Fi nal Ch o rd r a t i o f o r p r op e ll er A (C / R )i T ( 16 , I) Fi nal Ch or d rat io f or p r op eller C " T T Th rus t, Ib s . i HP c T 0 C omp r e s sor p owe r r equired to pump f rom P- sta ti c t o re qu ired hub j e t p r e s su re , H P _ H Ppc T1 To t a l c e n tri fu g al ho rs epo w er r eq u i r eme n t , HP !

T T2 Ambie n t tem p e r a t u r e, Degrees R T 3 To t a l us e f ul wo r k, ft - lbs i

HP i

ae r o T4 Aerodyn a mi c t o r q u e , HP i H Ptota I T5 T o t al pow er r e quir ed , HP !

i T T6 T hrus t d e v elo p e d , I bs .

T7 L ogi cal l l fb oth bl own & n o n -b l own e valua t i o n , i

0 = elthe r blown o r no n -b l ow n eva lu ation I

l Ca se T 8 Ca se i de n ti fica t i o n | 0--manual i npu t , i I-I0 predef i ned i n data s ta t e m e n t s I H P a v al I T 9 A va i la b l e h orse p o wer @ cur r en t e ngi ne s pe e d , HP (C _ ) _ U (I, I ) Mom e n t u m C oe ffic e nt s a t eac h b lad e s tat io n ] 49 ', - " _ 111 I II I' ±--. I r _ ] , ,;.! ENGINEERING PROGR A M US A G E - ' I U( 2- 7 ,I ) No t u s ed _! _¢ U(8,I) Ph i a t each bl a d e s t a tion , d egree s : U(9, I ) A lpha a t each b l ade s t a t ion, degrees _ = _ U(IO , I) K (1) in t h e Ind u ced vel o cit y iterat i ve equati o n , i _. a UO A n g le of A ttack i n li ft / dra g lo o kup s u br o u ti n e - 4 UI Te m p er a r y (loo kup sub_ ou t lne) l _ ; i _ U2 Vis c o sit y of a i r i U 4 Te m po r ar y variable h U 6 Tem po rary variable (Induced veloci t y equa ti ons) _ i (P _ ) U 5 To t al hu b p r es s u r e , Ibs / ft _ - # 2 t U9 Te mpo ra ry v a riable ( AT A N ar g u men t ) V_ V Free s t rea m ve lo ci ty , f / s _, V _ V(I) L o c al ve l oci t y at each b la de s ta t ion , f / s V 1 Te mpor ar y vari a b l e (Induced ve lo ci ty equa t i o n s) V2 Temp o rar y variable (I _ du c ed vel o c it y equati o ns) _ V3 Iden ti f i cati o n n u mber of first blade s tati o n _ used in cal c ulati o n o f n o n-bl o wn p ro pel l er ' ] _ lif t and drag c o efficients ,_ i • • V 4 L o gica l= O=Blown , l=Non-blown i V 7 L o gical = Ind u ced velocity ite ra ti ons c o mple t e? I_ l=ye s , 0=no.

J V8 Log ical: D _g onis t ic printer ou t p u t des i red?

l fye s , 0=no _ ' V 9 Lo_ £cal = A naly t ic o utput c o mplete? l=ye s,, O=no |_ ) N 2 Logica l= W a n t CRT i tera ti ve ou t pu t ? lffi y e s X(I) x-i , Ome g a*R / V Y Te m porary var i able Z(I) S im pson' s r u l e t ransfer parame t er array. (Value of i_ e g rand a t each s t a ti on.)

Z Simp s on' s r u le integral (Integral of Z(I)) O tef. 4 ) Z0 Displacement Velocity Ratio Z9 De g ree s / Ra dian co nvers io n fa cto r.

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V

ORIGINAL P A G EI W 1

O F P O ORQUALITY |

P rogr a m Listing and Cross Refe r ences j 1 0 R EM_****_,_w*_,_***_*****_*_-_,_-k_-_e_-k .!

20 RDt* * " 3 0 R EM * PRO PE LLOR DESIGN P R OGR A M F OR USE IN * i 4 0 R E M * THE DE S IGN OF A FULL-BLO W N PROP OR A NON-BLOWNPROP * _ 50 R EM* WHB L AR C 1 / 1 8 / 83 * !

55 X_ * *

7 0 D IM E(20) , X(20) , F(20) , G (20) , R (20) , H( 9 , 2 0 ) , T(1 6 , 20) , Q( 1 0 , 3 0) 8 0 DIM M(2 0 ) , K (20 ) , U( I O , 2 0 ) , J ( 9 , 8) 60 REM W**WW _*_ '¢ * ' A ' WW*' ; _ r f C WWW*_**WW **** _WW***WW*¢_ ' _******W ' A ' _% " 2 ¢ ** _ _' I c _ i 90 DIM L(2 , 2 0 ) , D(4 , 20),A(4 , 20),Z(20), C (4 , 20) , B(20), V (20) I 00 RELY [ W.' : c ,W, . ' W c WWWWWWWWW.WW,WWW_ . ¢ W*WWW_ ;¢ W_ ¢ . -W _W_ c f ¢ W_ c WWWWWWW, I i 0 REM STA R T I N PUT OF VA LU E S 1 2 0 R E M _ ¢ * * * . _****e_ - _*_*_*****e_****_****_ r _ - *_m ' * 13 0 O P E N " OUTPUT.D A T " FOR OUT P UT A S FIL E #1% 1 4 0 MARGIN # I Z , 1 3 2 % 1 50 O PEN " C R PL O T.DAT " FOR O UTPUT AS FIL E # 2% 160 M A R G IN # 2 _ , 8 0Z 17 0 D A T A - .6 8 , 5 3 . 5 , . 2 6 , - I. 0 , . 00 9 , -.4 0 , -. 001 , 0.

1 8 0 D ATA - .42, 5 2. 5 , .2 7 ,-I. 0 , . 008 , - .4 0 , 0 .,0.

190 DATA -.1 5 , 5 1. 5 ,.28 , -2.0,.008,- . 40,.0009 , -.02 5 200 DATA .13,49. 5 ,.2 5 ,-. 5 0 , .0089,-.425,.0011,.02 210 DA T A .3 8 , 4 9 . 0 , . 28 , -3. 50 ,.01,-.40 5, .0031,.04 i 22 0 DA T A .66 , 4 5 . 5 , .26 , -5 . 50 ,. 01 31,-. 3 6 5 ,.0024,.0 7 5 t 230 DAT A . 9 2 , 40 . 0 , .24 , 08 . 00, . 0 1 55 , - .2 9 ,. 00 6 9 ,. 0 " 2 40 DATA 1.16,32.0,.1 7, -9.50,.0224,-.29 , .003 5, .02 2 5 0 DATA 1.33,22. 5 ,.0 7 ,- 5 . 5 0,.02 5 9,-.2 7 ,.00 7 7 ,.2 7 2 6 0 FOR I = I T O 9 _ 2 7 0 FO R J =l TO 8 280 R EAD J(I, J ) 290 NEXT J 300 N E X T I 3 1 0 D AT A 2 70 . , 41.6 , 6. , 3 24. , I0000. , 3 . , 0 . , 0 , I , 0 , 3 , 4 , 4 , 4 , 4 , 4 , 4,4,4,4,4,4,4,4,4 , 4 } 320 DA T A 4 , 4 , 4 , 4,4 330 DA T A 27 0 . , 41.6 , 6 , 32 4. , I000 9. , 3 ., 0 , I , I, 0 ,2, - 12. , - II.4 9 ,-I0 . 92 , -I0.38,- 9 .82 _,_ 34 0 DA T A -9 .2 9 , -8 .7,- 8 .12, - ; ;,- 6.76 ,-5 . 89 , - 4. 9 , -3 . 8 2,-2.72 r 2 " : _1_ 3 50 DAT A -1. 55 , - . 3 , 1 . 0 , 2 . 3 , 3 .6 2 , 5 .

| 2 60 D ATA 270.,41.6,6. , 3 24. , I0000.,3.,0.,0,I,0,3,2,2 , 2 , 2 , 2,2 , 2,2,2 , 2 , 2 , 2,2 , 2,2 37 0 DAT A 2 , 2 , 2 , 2 , 2 i 380 D A T A 2 7 0 , 4 1 . 6 , 6 , 3 24 , 10000 , 3 , 0 , I , I , 0 , 2 , -12 . , - II .49,-I0.92,-I0.38,-9.82 [ 390 DATA -9 . 29 , -8 . 7 , - 8 .12 , - 7 . 5 , - 6. 7 6, -5 . 89,- 4. 9 ,- 3 . 8 2,-2. 7 2 I 4 00 D ATA -1. 55 ,-. 3 , 1 .0 , 2. 3 , 3 .62, 5 .

41 0 DA T A 12 5 , 4 5 , 6 , 3 47 , 0 , 3 , 0 , 1 , 1 , 1 , 2, 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 ] 42 0 D A T A 125 , 45 , 6 , 3 47 , 0 , 3 . 0 , 1 , 1 , 1 , 2 , -12 . , - 11 . 4 9 , - 1 0. 9 2 , - 1 0.3 8 , - 9 . 8 2 4 30 D ATA - 9.2 9 , -8 . 7 , -8 .1 2 , - 7. 5 , -6. 7 6 , -5 . 8 9 , - 4.9 , -3. 8 2 , -2.72 440 DA T A - 1 . 55 , -. 3 , 1.0,2. 3 , 3 .62, 5 .

4 50 DA T A 125 , 4 5, 6 , 3 47 , 0, 3 , 0 , 1 , 1 , 1,2 ,2 , 2 , 2, 2 , 2 , 2 , 2 , 2 , 2 ,2 , 2 , 2 , 2,2 , 2 , 2 , 2 , 2 , 2 ,2 1 46 0 DAT A 125,4 5, 6 , 3 4 7 ,0, 3 , 0 , I , I , I , 2 , -1 2. , - 1 1 .4 9 , -I 0. 92 , -I 0. 38, - 9 . 82 470 D A T A -9.29 , -8, 7 , -8.12,- 7 .5 , - 6 . 7 6, -5.89,- 4 .9 , -3.82 , -2. 7 2 4 80 DAT A -1 . 55 , - . 3 , 1.0 , 2 . 3 , 3 .62 , 5 .

4 90 DA T A 125 , 45 , 6 , 3 47 , 0 , 3 , 0 , I,0 , I , I , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4, 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 500 DA TA 125 , 4 5 , 6 , 3 47 , 0 , 3 , 0 , I , 0,I , I , 2, 2 , 2,2 , 2 , 2 , 2 , 2 , 2,2 , 2,2 , 2 , 2 , 2 , 2,2 , 2 , 2 , 2

Sl

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51 0FO R I=l TO 1 0 OF POOR QUAL r IY

52 0 FOR J =O TO 30

5 3 0R E AD O ( I , J )

540 N E XT J 550 N E XT I 56 0 RE M CLEART H E ' AN AL YT I C O UTPUTCOHPLETE ' FLAG 5 7 0 V9=O 580 RE M RESET THE THR U ST M ATCH IN G P AR AM ETE R S 5 90 A3=O 60 0 A7 = O 6 1 0 N 3=0 : " 6 2 0 PR I NT , " DATE : " ;DATE$( O ) 63 0 RE M......... ENTERT H E CASE IDE NT IFI C ATION FOR THE CURRENT RU N .... : 640 P RINT "INP UT 'C ASE i t' ( I-I 0) FO R T HIS RUN , OR ' 0 ' FO R MANUA L I NP UT "!

65 0 INP U T T8 i 66 0 I F T8<= O TH EN G O T O 81 0 .; 670 I F T S >IO THEN T8 = 1 0 " 6 80 V =Q(T8 , 0 ) 6 9 0 NI fQ( T 8 , I ) " 7 00 D =Q(T8 , 2 ) i 71 0 TfQ(T S , 3) : 7 20 H 2fQ(T 8 , 4 ) 73 0 Bffi Q(T 8 , 5) 7 4 0 P I =Q(T8 , 6 ) 7 5 0 C 5 =Q( T 8 , 7 ) *.

76 0 B7 ffiQ( T S , 8) 770 C6 =Q(T 8 , 9 ) : " 780 C7=Q(T8 , 10) _D . : _ - _ _ 79 0 I F TS _ > O THE N GOT O 99 0 t '_- 8 00 REH I N PU T AI RSP EED I . / 8 1 0 PR INT "EN TE R AI RSPEED , V , IN F T / SEC "; I .

820 INP UT V z 84 0 PR INT " E NT ER RO TAT IO NAL S PE E D , NI , IN R PS" ; _ , _ 850 IN PUT N1 _ 8 6 0 R EN INP UT PROP DL_ IETER ;T : j 8 7 0 P R INT " E NT ER PROP. DIA M ETER , D , I N FEET " ; 830 REM IN P UT ROT AT IO NAL S P EE D i - '" 880 INP UT D 89 0 REM INP UT TH R UST 9 0 0 PRI NT " E NT ER T HR U S T , T , I N PO U ND S" ; i 910 INP U T T Ii 920 REM INP UT A LTITUDE (I N F EET) !

i 930 P RINT. " E NT ER AL TITUDE , H , IN FEET "I i | 9 4 0 INPUT H 2 9 6 0 R E M FIRST S E T OF I NP UT V AL UES A R E COMPLETE I 9 7 0 REH ._ . ; . _ . _ . _._ . _ . _ ; ._ .;.. _ . _ ; _ . _ . _ . _ . _ . _ . _ . _ ;_;. _ . _ ; _**_ . __ . _ . _ ' 980 REH ..... Z9 = DEGREES / RADIAN ..... { F 99 0 P3 ffi 3.1 4 1 59 2 7 , 1000 Z 9= 180.O I P 3 , !

1 0 1 0 R F H ..... H2 IS CONVERTED TO M E T R IC UN ITS ( I _) .....

1020 H2-(3 . 0 4 8E- 04 )* H 2 i 10 3 0 IF H 2 _47 TH E N 1 070 !

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106 0 R h_: ..... ATMOSPH E PI C DENSITY SUB R O U TINE IS C ALL E D ..... _, ?

1 070 G OS U I _ _9 3 0 10 80 I F T8 < > 0 Y I:E N GO T O 1 2 10 ! , _ 10 9 0 R EM ****' : _*_,_'*_-_ , '_'- ' - : _'_,_*****_-_-_*******_ n _'**_ , • * t"l_ II00 R EM INPUT .... C ON D SET DF VAL U ES 1110 REM ******** . _ c _ ' ***** * *****_ . _ . _*******_***** • •

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1120 R EM IN PU T NUMBF .R O F B LADE S ON P R O P - -- i : 1 130 P RI NT "EN TER N U MB ER O F B L ADES ON PROP , B" ; _ 1140 INPUT B I'.50 R E M I NPU T H ORSEPOWER 1 16 0 P RI NT "ENT ER EN GI N E H ORSE P O W ER , P" ; _ " 117 0 I NPUT PI 11 8 0 R _*****_. ' ,_._.'_-_ . _ , _ . ...-_-._ , _**-_._,_,_*****- , _- ,. _-********* ,i ' _ .

1190 R EM S E CO N D S E T OF INP UT V AL UE S A R E COM P L E TE _ . ; i 20 0 RE M **' : ' _, - ' • _ '. _."_. , _ ' _ * _,_ *" _ : _'_._ , _ _ . _ * _ " _ - _ " * _ 1210 RE M ..... R 6 = T IP R ADI US O F PROP .....

12 20 R6=D / 2 ] ]23 0 R E M ..... B1 = TH R UST CO E FFICIE NT _ E QN . 15 _ ..... | 1 2 4 0 BI =8 * T / (H'W** 2 * D **2*P 3 ) _ * 1 2 50 R EM B 2 = AD V A NCE ANG LE _EQ N. 9 > .....

12 6 0 B2 =V / (P 3 * N I*D) 12 70 R E M B 3 = POWER CO E FF I C I E NT 1280 B 3= 2*PI*5 5 0 / (H *V**3* R 6**2*P 3 ) 1290 FOR I=I TO 20 1 300 R E M ..... K (1 ) = RA TIO OF RAD IUS D I STANCE F RO M I TO T I P < EQ N. 1 7_- -- 1310 K(I)=0.05.I 1 3 20 NEXT I 13 3 0 REM BLOWN O R NON-BLOWN DESI G N 1 3 40 I F TS _> O TH EN G O T O 1420 1 3 5 0 R EM ****_ . _._ ' * MANUA L INPUT F OR BL O WN / N O N-BL O WN E V AL U AT IO N ** - A-_****_**-_._ 1 3 60 PRINT"EN T ER 'I' FOR NON-BLOWN PROPELLE R DESIGN, '2' FO R BLOWN D E S IGN," 1 3 7 0 P RI N T "O R '3' F O R B OTH .... " ; '_- 13 80 INPUT C7 _ 1 39 0 IF C7< I TH EN C7= I I_0 0 I F C7> 3 T HEN C7" 3 1 14 0 1 P R INT 1402 PRINT"ENTER CO D E FO R PA R AM E T E R YOU W ISH T O VA R Y IN MA TCHI NG T H RU ST S ." i 140 3 P RI NT"ENTER ' I ' FOR CHORD S C AL I NG, '2' F OR BETA S C AL I NG, AND " 'i 1404 PRINT"' 3 ' FOR ALPHA SCALING. "" , I 14 0 5 I N P UT C I 1 14 0 6 I F C I <I OR CI >3 T HE N G O TO 1 40 2 { 14 07 I F C I = I T HE N C5= 0 E LS E C5=I l 1408 I F C I = 2 T H EN B 7=O EL S E B 7= I I 1409 I F CI =3 THEN C 6 = 0 ELSE C6=I 1410 REM *** * * * N OW SE T UP CO NT ROL PARAME TER S FOR SE L ECTED E V A LU AT IO N _******* 1420 I F C 7 = 2 T H EN V 4 =O EL S E V 4 = I 14 3 0 I F C7 >= 3 TH EN T 7=I E LS E T 7= O i 1440 I F V 4 = 0 THEN V9= I ' _ 14 5 0 *EM***._*********** * ********************************************** . i 1460 R E M W A N T D I A G ON I ST IC OU T PU T??? I= Y E S , 0=NO I NT O V8 '_ !

14 70 * EM******************* * **************************************_-_**

5 3 c

g, ........ . _ i i ii I B II ORIGii _ I A L PA QE [ _ 148 0 PRI_"E_ E R 1 T O IN CLUD E D IAG O NI S TI C P RINT_ O UT P UT, " -, OF POOR QUAL ITy 1 49 0 P RI NT " O THF . RWISE F . _ ER '0' .. " ; 1500 I_ V8 151 0 I F V8 _ 0 T H E N V8=O 152 0 I F VS_I TH E N V8= I 153 0 PRIN T "ENT E R ' I' F OR IN FL OW I T E R A T ION CR T O UT P UT , O T HER W I SE ' 0 ' " ; 15_ 0 INPUT W 2 1550 I F W 2> l T H EN W 2= l 1560 I F N l _0 T HEN W 2 = 0 1570 R E M 1580 I F T S:> 0 THEN GOTO 1 7 90 1590 IF(T 7 =1) AND (V4=0) THEN GOTO 1820 1610 R E M MAN U A L INPU T O F A LP H a A T E A C H B L ADE S TA T ION 1 6 2D R E M 163 0 REM A(I , I) = B L AD E AN GL E OF A TT A C K 164 0 R L M A(2 ,I) = INTER V AL C ON ST AN TS 1650 R E M A( 3 , I ) = I N TER V AL I N CR E M ENTAL A LPH A 1660 RE M 1 67 0 R EM_ : . _ ': . : . _ : . _ . _ _ : . _ : . _ . _ ___._&_ _&_&___ __ A_ 1 680 I= 1 1 690 P RINT "AL PH A ( " ;I ;" ) " ; 1 7 00 I NPU T A1 1 7 10 PRI NT "H OW MANY V AL U E S OF " ; AI; 1 720 INP U T K 17 3 0 FOR J= l T O K + I - I 1740 A(I , J)=AI 1 7 50 IF J = 20 T HEN 18 20 1 / 6 0 NEXT J ._, 1770 l = J + l 17 8 0 GOT O 16 90 1 7 90 FOR I=l TO 20 1800 A ( I , I ) = Q(T 8 , I+ I0) 1810 NEXT I 1 8 2 0 Rh_M*************_****'#***********_***_._**********_ __ _ _ _r 1 830 REM N O W HAV E 2 0 VALU ES FOR A (I , I) [_ 1840 R EM A(I , I ) = 20 ALPHA V AL UES 1 8 50 REM ASSIGN L O OKU P TAB L E INT ERVA LS _ 1 8 6 0 REM . *************_'A_** ' : _**'_ n _*_A- ; .-A-_-_ m **_'A'_ a _ ; , _ - _____ _ r 1 8 70 A ( 2 , 1) = - 3 :

188 o A( 2 , 2 ):o i

1890 A(2 , 3);3 1900 A(2 , 4)=6 1 9 10 A (2 , 5 )=9 I 1 92 0 A (2 , 6) =1 2 i 1940 A(2 , 8 );1 7 1950 R l,_t*'_'*****_e - '¢**._'_ c _'*N'_'.' : '_'l q _'c*_"_ q ccc_t ' ;ecc'_ e _. ' _'_'_i__ _ _ _-A- __ _ _ .;_ ¢ , A_ AA_ A_ _ 196 0 RE M NOW A SS I GN LI FT AN D D R AG VA LU E S TO L OOK U P TAB LE C OE F F IC IEN TS 1 9 7 0 REMCo_co_**_c_***c_ : _*co_ ' _¢_ ' *c_"#_,__ _ : _ : _-_ _ :, _ _ _ _ ;,_ _ A_ _ _ 19 80 R EM , i 1 990 L(I , I )= 0.001 2 0 0 0 L ( 1 , 2) =0. 3 7 2 010 L ( I , 3) = O. 73 !

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5 4

l

ORIGINAL PAGEi g ]

OF POORQUALITY

2020 L(I , 4) = I.01 20 30 L(1 , 5 ) = 1. 3 2040 L(1 , 6 )=1. 5 2 - _ 2 0 50 L(1 , 7 ) = 1.66 20 6 0 L( 1 , 8) = 1.66 2 0 70 L(I , 9 ) = 0 .0 0 1 2 080 D(3 , 1 )= 0. 0 12 3 20 9 0 D( 3, 2) = 0.00 8 1 2 1 00 D(3, 3 ) = 0.01 2110 D( 3 ,4) = 0.0127 2120 D( 3 , 5) = 0 . 0 1 81 2130 D(3,6)=0.0242 2140 D(3 , 7)=0.036 5 i, , _ _ ,, i ,, f.j_, , _ , • ° • • • * * • , ., • • • , ° , , , ° , , , 2160 REM W E N OW HA VE I NTERV A L LI MI TS A ND LI N E A R COEFFIC I E NTS FO R T H E L I FT _ ; 21 7 0 REH AN D D R A G COMP U T A TI ON S ..... NOW C OMPU T E L IF T 2 1 80 REH ......... .Y.Y.Y.Y.Y.Y.Y.Y. * _-., , -'_ , ._ , -' , _----'-' x . ** __,_. , -A- c - : n_.,_ ................... _-_ , _ . _ ** _ w : 219 0 IF V 4 =0 T H EN G O T 0 2 540 2200 F OR I=l T O 20 2 210 T ( 4 , I ) =A ( I , I) 2 2 2 0 NEXT I 22 3 0 V3 = I

!

2240 GOSUB 8410 2250 IF V 9 = I T HEN GO T O 2540 2260 REM . ,_e - -ee .... _................................................... * . _ . .*_. . . . _. . '_.. - _-_.*__ 22 7 0 REM OU T PU T V ALUES T O PRINTER 2 280 R EH _ ' _Y , _ , _ .............. _ ,, * _ . , *Yr#_, . _...... , ......................... , _ , ,_.-_ 2290 PR INT #I ,CH R$ (12%) ! F O RM F EED 2300 P R INT #1% ,T AB(40)I"ANA L Y T I C RESU L TS F OR C ASE #": T8 2310 PRINT #I , " V"IV ; ! FR E E STREA M VE L OCI T Y 2 320 PR I NT #I , " N" IN I; _ E NG INE SP EE D , RE V / S EC 2330 PRINT #I , " "' • D , D , .PROPE L LER DIAMETER , FEET 2340 PRINT #I , " T" ; T; !REQUIRED THRUST , L BS 2350 PRINT #I , " RH0" ; H !AIR DENSITY , RH0 23 6 0 PR I NT #I 23 7 0 PRINT #I , " B " ; B; !NUMB ER O F PRO P ELLER B L AD E S -_ 23 80 PR I NT #I , " H , KM";H 2; ! ALT I TUDE , KM 2 39 0 P R INT #I , " P";PI ; !A V AI L AB L E EN G IN E HO RSE POWE R 24 00 P RINT #1 , " V / ND" ;V / ( N I _D ) _AD V A N C E AN G LE , L AM B D A , D E GRE E S 2 410 P RINT #I 2420 PRINT #i ," LAMBDA";B2; !A DV ANCE RATIO 243 0 PRI NT #I , " T C "IB I ; !TH RUS T COEFFI CI E N T 1 2 44 0 PRINT # I , " P C ";B 3 !P OW E R C O EFFICIENT 2 4 50 PR I NT #1 2 46 0 PRINT # I , "K SI CL D / L ALPHA " 2 4 7 0 PR I NT # I 24 80 FOR I= l T O 20 249 0 PRINT # I ,K( I ), C (1 , I),D(4,I),A(1,I) 2500 NEX T I 25 20 REM FIR ST OU T PU T C O MP LE T E , C O M P UT E F O R S E CO ND O UTPUT J 2530 RE M _ *e __ * _ * ____ * _*_Y_A_ .i i

" r 4

ORIGINAL PAG E ; _ .

OF POOR QUALITY - ' 25 4 0 FOR 1 =1 TO 20 2550 R E M ___ <EQN. 8P ____ - _ - _ .. e . e . _ 2 5 60 E(1 )=O.5* B*S Q R (B 2_ X 2+I)*(I-K(1)) / B2 2570 RE H _ - _ . _ ' r * . . _ - ' _ e _ < E QN 5 > __ ,' ____ 2580 X(I)=K( Z ) / B 2 2590 REM _ : __ < E QN 7 > _ , _ ._ , ___ - - _ 2600 Y = EXP( - E(Z)) 261 0 F(I)=2 *A TN ( S Q R (I- Y_'_ 2) / Y) / P3 .... "''**''*'* 2620 R EM _ - __w_ <EQ N 6 > _ t-. _ - ____ 2 63 0 G(I)= F (I)*X(1)** 2 / (X(I)_'_ 2 +I) 26 4 0 R E M _ , __ < E QN 2 0 > I NTE GR AND __ , , " * ,' __ 2 650 M (I ) = 4*K( I )*G( I )*(I- D (4, I ) / X( I) ) !

2660 NEXT I 267 0 FOR I = l T O 20 2 6 80 Z( I ) =M (I) 2690 N E XT I 2 7 0 0 GOSU B 883 0 27 1 0 REM _ ' _ ' __ < E Q N 2 0 > I NTEG R AL _____ 2720 M = Z 2 7 3 0 F O R I = l TO 20 27 4 0 R EM ' : _ < EQ N 21 > _NT EGR A ND -_ : __*_ 2 7 50 Z(I)=M( I ) / (2*(X(I)_'_2+I)) 2 7 60 N E XT I 2 77 0 G OSUB 8830 2 780 REM _ < EQ N 2 1 > I NT EG RA L _____ 2790 N=Z 2 800 FOR I=l T O 20 281 0 RE M _ ' _ ' _ < E Q N 16 • I NTE G RA ND , FI RST PART _'_ 28 2 0 Z( I)= 4* K (I ) *G (I) * ( I + D(4, I )*X( I )) 28 30 NEXT I 2840 GOSUB 88 3 0 i 2 8 5 0 R EM _ . __ _ EQ N 16 > I NTE G RA L , FI RST PA RT __ ' _ * 2860 O=Z 28 70 FOR I= l T O 20 _ * 2880 R EM * *** * *** * ***** _ EQ N 16 > iNT E _RAN D . SECO N D PA R T _ * _ * _ * * * * ....

28 9 0 Z (1 ) = 4* K ( 1 )* G(1 )* (I+D (4. I )* X ( I ))*X( I )_'_2 / (2*(X( 1 )_2 + I)) 2900 NEXT I 2910 G OSUB 883 0 2 9 2 0 RE M _ w _ . , . _ .c - t _ < E QN 1 6 > I NTE G RA L , SECO ND PART e_-_-_-_m-_ - m _ 2930 P=Z 29 4 0 I F T=O T HEN 30 70 2950 REM ,_ . ** * _ -, _ , __, - _r . ;_ - ____ 296 0 REM T HE R EQ UIRED TH R U S T WA S SP E CIFI E D 2970 REM _ ; _ , _ , _& , _ , _,__ , _ , _ * **_ , __,_.___ 2980 R E H 29 90 REM **** ** *****_ < EQN 1 9> ****_.___-_ ; _ ;;; _ ;; 3000 Z O= M_ (I - SQR(I-( 4*B I * N / M _*2))) / (2*N) 3010 R EM **** * ***_ w _-_, < E QN 2 9> N UME R AT OR _ : . __ ; __&&_ 3 020 B 3= O* Z 0+P*Z0** 2 3030 R E M _' * __ ; < E QN 29 > "_";_ * ___ , __ . _ & _ , l I 3 0 4 0 BS = BI / B3 , f 3 050 GOTO 3160 !

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J

F-"

O R I GINAL PAGE _3 _ ; OF POOR QUALITY " ' 306 0 RE M "A'_ ' ' r : c Y' - : ¢ _'c ' ' _'_¢_'_W " _ _ " " "_'c _ ' _ Yc * ' ' : Y'_ ' ' _ ' c ' ' t_ ' _ _ 'H c Y c '_ _ Y_ ' _ _ _ W _ _%" _%_ _ _V _ _ _ 3070 RE N THE ENG I N E HORSEPO W ER W A S SPECI FI ED ..o . i . .,o .., o _.,o . o . _o . _ ,,.l_o .. ._,_..qb,.,%_..t v .i o °, _ ° .,o • • . _ . _ L , ..

3 080 R EM ,r, _ , r ..... r A'Y ¢ ....._ ...._%_,' ¢ , , , ,_ ..... : _ : , _ r }_Y ¢ _'_%Y r Y{_' Y _ / , c _ , _,_" AW ,_ r _,_ , _,,,_% 3 0 9 0 Z0 = O *( S Q R (I_ ( 4 * B 3*P) / O **2)-I) / (2*P) 3100 BI=M*Z0-N*Z0**2 311 0 R EM ................... . _ ....... _ . _ .......... H _ < E QN 2 9 > **Yn'_*****e*"_"_"_"Y H r ***************_ } 3120 B5 = BI / B3 _ , ' 313 0 R EM*Y : ** .w _* . _ . . . _ .................... Y , r_ . _ .: . . _.. ' . .'*_ . . . _ ........ ****** . . . .**_._*********** 3140 R EM B E GIN S E COND S ET OF O U TPU T S 316 0 IF V9=l THEN 3210 31 70 P R INT #I _ : 31 8 0 P R INT #I , " Z "IZ O ; _ 3190 P R INT #I , " ETA";B5 _ 32 00 RE M - : _ . _ . . _ . _w_****** . Y_ . _ RE Q U I R ED TOR Q UE F OR CURR ENT PRO P ELLER _r_, i 3210 Q6 = V_'_*3*BI*H*D**2 / (16*NI*B5) , 3220 REM _'_*_'_ : :********** REQUIRED HORSEPOWER FOR CURRENT PROPELLER * 3230 PI=2*P3*NI*Q6 / 550 3240 REM _ , _ , ',**_' , - : _*Y , _' , '***_'* T H RUST PRODUCED BY CURRENT PROPELLER ****** 3250 T=2*P3*NI*Q6*B5 / V " { 3260 IF V9=I THEN GOTO 3370 3 2 7 0 P RI NT #I 3280 PRINT #I ," TORQUE"IQ6; 3 290 P R INT #I , " HP";PI; 3 3 00 PRINT #I ," THRUST"IT 33 10 RE M . . . _............................... _ ........................................................... _*'_**** , ,_ ..... _ ': , ,** , ,*** , .

33 2 0 R EM** ** 3 33 0 REM** BYP A S S ANALYTI C C HORD A ND BETA C ALCU L AT I ONS ** 3340 REM** IF OFF DESIGN EVALUATION (T8>4) ** <" 3350 REM** ** 33 6 0 a_'* ............................................................................................... _. .: ........

3 3 70 FOR I = I TO 20 33 80 R EM '"*** ' :: * ' :: "_* ' :: *** < EQN 24> ......................................................................

33 9 0 I F T8<5 THEN C ( 3 , I) = 4*P 3 *B2*G(1)*Z0 / (B*SQR(X(1)**2 + I)* C (I, I )) 3 4 0 0 R EM ....................................... < EQN 25B> ....................................................................

3 410 IF T8<5 THEN B(1) = Z9*ATN(B2*(I+Z0 / 2) / K(1))+A(I,I) . < _ 3 420 R EM ********* S AV E CA L C ULATED AN A LYTI C VALUE S FO R SU BSEQ U ENT CAS E U SE *** ; 3430 IF (T8=I) AND (V4=I) THEN T(5,1)=B(1) 3440 IF ( T8=2) T HEN C(3 , 1)=T(15,1) { 3 45 0 IF ( T 8 = 3 ) AND ( V 4=l) THEN T(7 , 1)=B(1) 3460 IF (T 8 =4) THEN C(3,1)=T(16,1) !

3 4 7 0 IF (T8= 5 ) T HEN B(1)=T(9,1) i 3480 IF (T8=5) THEN C (3 , I)=T(15,I) 3490 IF (T 8= 6) THEN B(1) = T(6,1) I 3500 IF (T 8 =6) THEN C(3,1)=T(12,1) I 35 1 0 IF (T 8=7) T H EN B(1)=T(10,1) i 3520 IF (T8=7) THEN C(3,1)=T(16 , 1) 3 5 30 IF (T8=8 ) THEN B(1)=T(8,1) i 3 540 IF (T 8= 8 ) T H EN C ( 3 , 1) = T(14,1) 3 55 0 IF (T 8=9 ) THEN B(1 ) =T( 5 ,1) _ 3 5 60 IF ( T 8 --9) TH E N C (3,1)=T(II,I) ,i 35 7 0 IF (T 8 =I0) T H EN B(1)= T ( 7 ,1) 358 0 IF (T 8= I0) THEN C ( 3 , 1 )=T(13,1) 3590 NEXT I 57 _!

ORIG I NAL P AQ E II

OF pOORQ U AL I T Y

36 00 IF V9 = 1 T HE N GO TO 3670 3610 PRINT # I 3620 P RI NT # I , "C / R .5 ( C / R) C OSB .5 ( C I R)SI NB B " 36 3 0 P R INT #I

364 o F OR I = 1 T O 2 O

365 0 PR INT #1 , C (3 , I) , 0 . 5 * C (3 , I)* COS (B(I) / Z 9) , 0 . S *C(3 , I)* S IN( B (1) I Z9) , B(I) 3660 NE X T I 367 0 GO S UB 8 9 3 0 3680 REM, VELOC I TY OF S OUND (IN FT / SEC) 36 9 0 C2 = S QR ( Z 4 0 3. 0 * T 2) 3700 REM V I SC O S ITY (L B* SEC / F T** 2) 3 7 10 U 2=(340.8+0.548*( T 2-453.0))*(10**(- 9 )) 372 0 F OR 5=1 T O 20 3730 R EM . ***_**** LO CAL V EL OCI TY , F / S ****_ ' ___ 3 7 4 0 V(1)=SQR(V . _'_ ' _2 + (2*P3*K(1)* R 6*NI)**2) 37 5 0 RE M M AC H NUMBER 37 60 M(1) =V (1) / C 2 3770 REM R EYN O LDS NUMBE R 37 8 0 R (1)= H *V(1)*C(3 , 1)*D / (2*U2) 3 7 90 NEXT I 3 8 00 IF V 9=I T H EN GOTO 38 7 0 3810 P R INT #I 3820 P R INT#1 , "MACH NO R EYNOLD S NO" 3830 P RI NT #I 3840 F OR I=1 T O 20 ,- 38 5 0 P R INT #I , M(I),R(I) 3860 NEXT I 3870 REM SET ' A NA L YT IC OU TP UT CO MPL ETE ' F LAG T O I "_: ' 3880 V9= 1 3 89 0 RE M _ : _ _ " _ " " _ ....................................... _ ** _............ _ , , , _ , _ ,, _, _ , _*** , , , , *_w , o_ x ****'_**** 3900 R EM* CALC UL A T E EA CH B LAD E S T ATIONS LOCA L V E LOCI T Y [EQ N. 7] I 3 910 REM_*_.** . . * * * * **** * ******************* =.***_'_* _ - _ . .__ . _********* 3920 REM 39 30 FO R I=I TO 20 F , ' % 3940 H(3,1) = (V**2+(P3*K(1 ) *D*NI ) **2 ) _ ' _ ' .5 .... ' _ 39 5 0 NEXT I .

39 6 0 RE M*_`**_ ` _ ` _ ` _*_****_ `x _`_ : *_****_********____ 3 9 70 R EM** ** i 3980 RE M** ROU TE P RO GRAM F LO W BA SE D ON BLOWN OR NO N - B L OWN O P TIO N ** 3990 R EM** (B L OWN , V 4 = 0; NO N -BLO WN , V 4 =l ) ** I 4 000 R EM** ** 401 0 R EM***_ **_ ` ****_ _**_` _` ***** *__*** _ **_ ` _***e_v*_` _********Yr_***_******** 4 020 R EM*_******* SE T T H E J ET VELO CI T Y AT T H E T I P TO . 95 M ACH **_ex-_,, 40 30 R EM********** I F BL O WN AND T H E DES I GN POI NT EVA LU A TIO N **_-_**_-A_***_ 4 0 40 RE M********** O T H E R W IS E, SH UT BL O W ING O FF **__**_,Y_eA-A-A-_, I 405 0 R EM I 4 060 IF (V 4=0) AND ( T_5 ) T H EN H( I,1 9) =. 9 5" C 2 E LS E H( I,1 9)=O . !

4 07 0 R EM 4 080 R EM********** T HE R E QUIRE D JE T P RE S SU R E AT ST AT IO N 1 9 IS [ EQN 2] ** * _ 4 090 RE M , i 4 1 00 H ( 2 ,1 9 ) =0 .5*H* H (I,1 9 )**2. + P2 4110 R EM !

J

'i ORIGINAL PAG _ i_ ' ; OF POOR QUALIT Y " _ 466 0 REM 46 70 REM D EFI N E P H I(I) AN D O T HER QU A NTI T IES TO S TA R T I T ER A TIO N 46 80 R E M 469 0 B2 fV / (. P3* NI * D) _ L A M B DA 47 00 FO R I=l TO 2 0 4 710 U(8 , I)= A TN( B2 / K (I ) ) : P HI (I) [E Q N A l l 4 7 20 A (I,I)= B (I)-U(8 , I) *I 80 . / P3 ! C A L C UL A T ED ALPHA [E QN A 2] 4 7 3 0 T ( 4 , I)f A (1 , I ) . ' ALP H A ( I ) , CORR E C T ED 474 0 N EXT I 4 7 5 0 T ( 2 , 20) =0. ! a ' AT E L ;H S TA TI ON 476 0 T(3 , 20)=0. ! PHI , C O RRECTED i 4 770 T( 4 , 2 0)=U(8 , 2 0 ) : A LP HA , CO RR ECTED 47 80 T(I , 20)= 0 . ! a A T E A C H S T A TION 4 7 9 0 A(l , 20 )ffi O. ! A L PHA AT BLAD E TIP 4 800 R E M 481 0 RE M I N ITI AL IZ E ITER AT IVE E Q U A TIONS 4 8 2 0 R EM 483 0 V 7 = l 4 835 R E M -_ . _ ,' _ . c_'_ : _ - _ [E Q N A 3] _'___ i .

484 0 FO R Iffil TO 1 9 4 850 H(e , I)fSI N (U( 8 , I )) 4 8 6 0 H ( 7 , I )=C0S(U(8 , I)) 48 70 Vl f((( B / 2)*(B2"_ 2 +1 . ) ¢ ' * . 5 ) / B 2) * ( 1 .- K ( I)) 4 88 0 U 6 fEXP(-V l ) 4890 U 9 = A T N ( S Q R ( I -U6 **2 ) / U6) 4 910 U (10 , I)= B* C(3 , I) / (8 *P 3 *K (I)) * I . / (2 / P 3 * U9) 4 92 0 NEX T I ,, 49 3 0 V 3= l 4 9 40 I F V 4 = 0 TH E N G 0$U B 9 200 ELSE G O S U B 8 410 ' " 4 95 0 FO R 5$= "# # ## ### , ## ## # . ## ### . ## ### . ## # . ## # - ##4 H t # . # ###### " 4 9 6 0 R EM _ P,w, __ a ,_ w _- , _,_ w, __ . . _ . ., _ P , ,, _ ,,- ._ 4 9 7 0 RE M * _ ,.II _ T ; "_ . _ _ 17 D E G ( N O N - B LO _ ) OR 14 D E C. ( BL O I _ ) * 49 8 0 REM _*_'_ . ___ . _ , : . : . ; . _ ' _**___ 4990 F OR I = l TO 1 9 : " 5000 I F V4ffi0 T H EN C9 = 14 . 0 E L SE C9 = 1 7 . 0 - ._ 5 0 1 0 IF I > 19 T HEN C 9 =17°0 ?

5 020 I F (V 4 = O ) A ND (I<2 0 ) TH EN C I =1. 4 E LS E C I = 1 . 66 5030 IF A(I , I)>C9 TH E N C8=CI E LS E C8=C(I , I) 5 0 4 0 R E M **_***_** [EQ N A4 ] & [ E Q N A 5] _*_**.__' , _ - _ 5 0 5 0 V I fC8 *H ( 7,I) / H (6 , I) *-2 5 0 6 0 V2=C8 / H(7 , I) 5 070 T(1 , I )=(U( I O , I ) * V1) / (1.-U( 1 0 , I ) * V1) 50 8 0 T ( 2 , I ) =(U(IO , I )*V2) / ( 1 . + U (IO , I)*V2) 5090 REM **_ w _** [ E Q N A 6] _*********_*******¢_*_ ' _***_-_ 51 00 T ( 3 , I) ffiATN (( B 2 / K (I ) * ((I+ T (I , I)) / (I-T(2 , I))))) 5 1 1 0 REM ****_***** [ E Q N A 7] . _* - _ . . P t _ -- , w, ** . t _ ., . _ - _,_**_ , _ - ** - , ', -, P _ .P. , _ 5120 T( 4 , I)= A (I , I)+28 . 65 " (U(8 , I)-T(3 , I ) ) 5130 R E M _'_*******_ IF REQU E ST E D, O U TPUT CRT DI A GONISTIC D A TA _* 5139 IF W2< >I THEN GO T O 5 1 5 0 51 4 0 IF I>l TH E N GOTO 51 4 3 5141 PRINT 5 14 2 PRI NT " V 4 I AOA-I A O A -C P H I - I P H I-C C-MU C ! IC _• : / RA D" 5 14 3 P R I NT USING FO R 5$ , V 4 , I , A ( I ,I) , T(4,I) , U(8, I) * zg, ( B (I)- T ( 4 , _ ) ),U ( I _ i ) ,C(3,I) i 5 1 50 NE X T I % O RIG tN A L P A G E [_ OF P O O R QUA L I T Y _ 5 1 70 REM _** D I AG O N S TI C PRINT ER O UTP U T ****_ _ 5 1 8 0 IF V8< >I THEN G O TO 52 70 !

5190 P RI N T #1% , " I A O AI AOA C PHII PHIC A (I ) A ' ( I ) " 5200 FO R I = 13 TO 15 5 21 0 PRINT #1% USING '## # #_# # # ##.### ##.### ##.### ##.### ##.####',& I,A(I , I ) , T(4 , I ) , U(8, I ) *I 80 / P3,T(3,I ) *I 80 / P3,T ( I,I ) , T(2, I) . ,_ 5220 N E XT I ._ 52 30 REM _ E ND O F D I A G O N I STIC OU T PU T A T TH IS P OINT _ - _** 5240 REM i 5 250 R E M TEST ALP H A- A LP H AC FO R C O NV ERG E N C E _ : 5 260 REM _ 52 70 FO R I = l TO 19 i 5280 REM ", ,_ . _***¢_* [EQN A9 ] **_ ' c******************************_._**¢_*_ ' _ ' : *** 5290 IF ABS(A(I,I)-T(4,I))>0.5 THEN V7=O i 53 00 IF V8 < >l THEN GOTO 5330 531 0 IF ABS(A(I , I)-T(4 , I))>.5 T H EN PRINT " I , A(I , I) , T(4 , I) = "; I , A(I , I ),T(4, I ) 5 3 2 0 REM****¢_*** [ EQ N A8 ] UPD AT E C URR EN T P HI AT E A C H B LA D E ST A TION *_'**** ! -" 5 3 30 U (8 ,I ) = (B(I)-T(4,I))*P3 / 180.

5 3 4 0 R EM .............. UP DAT E CU RR E NT A LP HA GU E S S *** * ***********************'_ ' ***** • ¢ . ._. . ,* , . _ . . _ 5350 A(I , I)=T(4 , I) 5360 NEXT I 5370 V 3=I 5 38 0 RE M " _ '' _ " .... GEt N E W C 1 & C d VALUES F OR B LO WNO R N O N- BLO WN PR OPE LL ER*_* 539 0 IF V4=0 T HE N G OSU B 92 0 0 EL S E G O S UB 8410 54 00 IF V7 =0 TH EN G O T O 48 3 0 E _SE GOTO 5430 5410 REM 5 420 R EM E ND O F IT E RATIVE SE C TIO N .

54 30 REM ' - 5440 R EM CA LC U L ATE DIFFERENTIAL T HRUS T AT EA C H STATION, I , AND 5450 REM DIFFERENTIAL TORQUE AT EACH STATION .....

546 0 RE M _ F 5 470 FOR I = I T O 20 5 480 H(6,1)=SIN(U(8,I)) 5490 H(7,!) = COS(U(8,I)) _ 550 0 RE M ************ [EQ N 9 ] DIFF ERE NTI A L TH R UST ***************************** .e_ 551 0 H(4 , 1 ) =0 .5*H*V**2*((I+T(I,I)) / H(6,I))**2*B*C(3,1)*D / 2 5 52 0 H (4 , 1) = H(4,1)*(C(I,I)*H(7 , 1)-C(2,1)*H(6,1)) !

5530 REM************ [EQN I0] DIFFERENTIAL TORQUE **************************** 55 4 0 H( 5 , 1 )= D*K(1) / 4*H*V**2*((I+T(I,I)) / H(6,1))**2*B*C(3,1)*D / 2 _ i 5550 H(5,I)=H(5,I)*(C(I,I)eH(6,1)+C(2,I)*H(7,I)) [ 5560 Z(I) = H(4 , I) _ I 557 0 NEX T I 55 80 R EM I !

5 590 R EM I N T E GRATE DT / DR T O FIND TOTAL THRU S T, T6 5600 REM 1 5610 G O S UB 88 3 0 1 5 6 2 0 T6 = Z*D*0.5 I 563 0 REM _********* T E ST F O R CO NV E R G EN C E O F AC TU A L THR US T T O R EQ U I R E D T HRUS T _ : !

5 64 0 IF ABS ( T-T6_ T / 100. THEN a8=O ELSE A8=I i 5650 IF (T8>4) OR (A8=0) THEN GOTO 6 5 20 ,!

!

5 655 P RI NT . i !

6 1 ORIGI N AL PAGE I S O F POOR QUA L ITY • , _ , • • L_,. • , • • • * • • • _.. , .e..i . . • , _. ., • • • • • •-- o ° ° ° -- ° •-- , , - , • ° ° - , i_. , ° • , __ ° • _ ° L - , 5 6 6 0 R _ __._ . _ r __c e _ .....................................................

5 6 7 0 RI_I ¢_ 5680 RE M _ SCALE A LP HA , BET A , O R MOM EN TUM COEFFICI EN TS DEPENDIN G _ - _ 569 0 REM _ e _ O N C A SE BE ING R UN... T H E C O N TR OL V AR IA B L E S A R E A S F O L LO W i _ ' _ 5700 RE M _ C 5=I (C A SES 2 , 4-1 0 , & B LOW N C A SES) DO N OT RE SC AL E C H O R DS 5 710 RE M ¢_ B 7 = l (C A SES 1-8) D O NOT R E SC A LE BETA 572 0 R EM _ - _ C 6=i (C AS ES I N , 3 N , 5- 1 0) DO N O T R E S C AL E A LPH A _ ' _ 5 7 30 RE M _ AL L Q UAN TITI E S AR E R E S C A LED B Y RE Q UI RE D TH R UST / A V A IL. T H RUS T _ 5" / 4 9 RE M _ ** 5 760 RE M 577 0 RE H _ PR I NT I )I A GO N I ST I CS HERE I F V 8 =1 _-- ; ,_ ; , _ : .- _- ,;- _-_ r _ 5780 IF V8< >i THE N GOTO 58 6 0 5 7 90 PR I N T # 1Z , " REQ UIR E D T HRU ST = " ;T;" A V A IL AB L E T HRU ST = ";T 6 5800 FOR I=13 TO 15 5 8 1 0 IF C 5 <> I T H EN P RI N T ,_1% , "AL P HA V A LUE S A R E " ;I , A ( I , I ) 5820 IF B 7 <> I TH E N P R INT # 1 % , "BE T A V A L UES ARE ";I, B( I ) 5 830 RE M 5840 NEXT I 5 8 5 0 R EM E ND O F D I A GO N ISTIC OU T P U T AT T H IS P O I NT 5860 IF B 7=I THEN 603 0 I 5870 RI_ ¢_¢_'_*¢_'_ ' ,__*¢_¢_'_ . _'_' , _ - __ !

i 5880 R EM * R E S C A LE B ETA TO M AT CH A VA IL A BL E T H RUS T TO R E Q UI RE D T HRU ST 5 8 9 0 RE R _ ,': *¢ r _' r _***-_ ' ,'-_***__'_._'_'_-_-_:_' c __ 59 00 A2= . 0 05 *( T -T 6 ) 59 10 P R I NT " RE Q UIR ED T H R U S T= " ; T; " AVAIL AB L E T HR U S T = " ; T 6 ; "AU T O D E LT A B ET A = " ; A 2 5920 PR INT" T OT A L C HA NGE I N BE T A SO FAR T H IS R U N IS ";A 3 = 5 9 30 P R INT " E I_ E R ' 0' IF OK , 'I' TO ENTE R MA NUAL CHANG E I N BE TA, " i 5 9 4 0 PR IN T " OR '- I ' TO F ORCE E ND OF RUN. .. " ; I 59 50 INPUT A4 59 60 IF A4 = -I THEN G O TO 6 520 I 5 9 70 IF A4 = 0 T HEN GO T 0 6000 5 9 80 P R INT " E NT ER NEW C HA NGE IN BE T A ( DE G R EE S ) " ; 5 99 0 I NPUT A 2 I

I

6010 PRINT " TOTAL C HAN GE IN B ET A NOW IS "; A 3 603 0 IF ( C6= 1) O R ( V 4 = 1 A ND T8> O) THE N G O T O 62 00 6 000 A 3= A 3+ A2 - ,! , 6040 R EM __-__-____A_____ 60 5 0 R E M * RES C A L E A LP HA TO M AT C H A V A IL AB L E T HR UST T O RE Q U I RED TH R U S T * 6060 R EM _ e/e ___-_o____-_-_ - A - _ ' _ ' _ ' _ ' _ ;, _ 6 070 A6= . 0 35 _( T-T6 ) 608 0 PRINT" RE QUIR E D T H RUST = ''; T ; " A VAIL AB LE T H RUST= "; T6 ; "AUTO D E LT A AL PH A = " IA 6 609 0 PRINT"TOT A L C HAN G E IN ALP HA S O F AR THIS RUN IS " ; A 7 6100 PRI N T" ENT ER '0' IF O K, 'I ' T O E N T ER M A NU A L CH AN G E IN A LP HA," 6110 PRINT "O R ' -I ' T O F O RC E END O F R UN..."; 6 1 20 I NP UT A 4 613 0 IF A4 =-I TH E N G O T O 6520 61 40 IF A 4 =0 T HE N G OT O 6170 I 6 _ _ 0 P R I N T " E NTE R N E W C HAN G E I N A LP HA "; 616 0 I NPUT A 6 .I 61 7 0 A7=A7+A6 J 6180 P R I NT "TOT AL C HAN GE IN 'AL PH A' I S N OW " I A 7 , 6200 I F (T8<5) OR (T8 _ ) TH E N G O T O 639 0 !

_=_ -- ' ....... ',, , _ , - ,,. _ , . , -' '_ ' • . . _ ' . ,I ; 4 ,,' : ' _:_ _ - "" : - _ - " - "_" " ,' O R IGINAL PAG _ _ 3 , v j l OF POO R QUALITY _! ' ; I , 6210 R EM ********************************************************************* 1 " _ 6 2 2 0 R E H * RE S C ALE E N GINE R P M T O H A T C H AVAILAB L E T HR U ST TO REQU I RED THRUST * 6 2 4 0 N2= 0 .015*(T6-T) :i 6250 PRINT"REQUIRED THRUST=" ,T, AVAILABLE THRUST=";T6;" AUTODELTA SPEED=";N2 626 0 P R INT "TOT A L C H A NGE IN SPEED SO FAR THIS RUN IS " ; N3 ?

627 0 PRINT "ENTE R ' 0' IF OK , 'I' T O ENTER MANU A L C HANGE IN SPEED," _ _ . : 62 8 0 P R INT "OR ' - I' T O FO R CE END O F RUN .... " ; 6290 INPUT A4 6 30 0 IF A4 = -I T H EN GOTO 6 5 20 i 63 10 IF A 4= 0 THEN GOT 0 63 40 6 3 2 0 PRINT "ENTE R NEW CHANGE IN SPEED (RPS) "; 6 33 0 INPUT N2 6 3 4 0 N3 = N3+N2 _: 6 3 50 PRINT "T O T A L C HANGE IN SPEED IS NOW ";N3 i 636 0 HI=HI+N2 i 63 7 0 GO S UB 964 0 i 638 0 P R INT "AVAILABLE H O R S E POWE R IS " ; T9 I 6390 F O R I = i T O 2 0 I 64 0 0 R EM __ : _ : _ : _ : _ " _"_ ......... : ................. : _ ...................... _....... : . . . t . . ._ .............. ** .......... * .... _ , ..* _* , , _ , '_ 6 410 R EM * RES CA LE CHORDS TO OBTAIN REQUIRED THRUST * 6 4 20 REM ..................................................... _.......................................................

6422 IF B 7 < >I THEN B(1)=B(1)+A2 1 6424 IF (C6< >I) AND (V4=0) THEN B(1)=B(1)+A6 !

i 6430 IF ( C 5<>I) AND (V4=I) THEN C (3,_)=T / T6*C(3,1) _i 6431 IF ( C 5<>I) AND (T8=0) THEN C(3,1)=T / T6*C(3,Z) 6440 NEXT I 6450 REM _ . _ . . . _ : _ . .: _ ..... : _ . _ . . _ ...... r ...... _ . .. : .............. _, : ............ _ : _ ...... : . . . : .. _ : _ : _ . _ . _ . _ . **_ t _ : ,_ . .: _ : 646 0 REM ** ** 6470 REM ** FOR SCALED VALUES, PROGRAM FLOW GOES TO INFLOW ** 6480 REM ** ITERATIONS ** 6490 REM ** ** 6500 REM ............................................................................................... _ ........

6501 IF W_ >I THEN GOTO 4560 6502 IF (C_I) AND (V4=I OR TS=0) THEN P R INT" CHORDS HAVE BEEN RESCALED" 6510 GOTO 4560 6520 REM ' r : 653 0 REM INTEGRATE DQ / DR TO FIND TOTAL TORQUE, Q6 i 6540 REM 6550 FOR I=l TO 20 6560 Z(I) = H(5,I) 6570 NEXT I 6580 GOS U B 8830 6590 Q6=Z*D*0.5 6600 R EM 6610 R_ ! SET BLOWING HP V ALUES TO ZE R O F OR NON-BLOWING CASE 6620 REM 6630 T0=O.

6640 TI = 0.

66 5 0 REM 6660 REM SKIP B L OWING C AL CU L ATI ON S FO R N O N-B L OWN CASE (V4=I) 6670 REM ' _ !

6680 IF V 4 =l THEN GOTO 7030 [ 63 i t t

f . I L

ORIGINAL PAG Ei S

OF POORQUALI' r_

66 9 0 R E M 670 0 RE M CALC U LATE T HE MA SS FLO W P E R FOOT (H(8 , I )) A N D T HE 67 10 R EM HORSEPOW ER PE R F OO T (H( 9 , I)) REQUIRED... 6720 REM 6 7 30 FOR I = I TO 20 67 4 0 IF 1 > 19 T H EN GO T O 6 820 6 7 50 IF H (I , I) >O . T H E N GO T O 67 90 676 0 H(8 , I)=O 6 770 G O T O 6 8 10 67 80 REM ........... " ........ [ E QN II ] , _ - _..._r** . .

67 90 H ( 8 , 1) =U (I , I )* C ( 3 , 1)*D / 4*H*H( 3 , 1 )**2/H(I , I) 6800 REM *******_*_******** [ E Q N 1 2] *******_'_****** 6 8 1 0 H ( 9 , I ) =H (8 , 1 )*6006.* T 2*((H(2 , 1 ) / U5 )** .286-1 )/ 55 0.

6 820 IF I>19 THEN H(9,1)=O 6 830 IF 1 >19 T H E_ H( 8 , 1 ) = O.

6 8 4 0 Z(I)= H ( 9 , I ) 6850 NEXT I j 6 8 60 REM 687 0 REM INTEGR A TE H P R E QUIR ED / FOOT T O F I ND TO T A L HP , TI 6 8 _ REM 6 8 9 0 G O SU B 8830 I 690 0 TI =Z *B* D * .05 69 1 0 RL_ 6 920 R EM I NTE G RATE M A SS FL O W / F OO T TO F I ND TOT AL MASS F L OW 6 930 REM 6940 F OR I=I TO 20 6950 Z( 1 )=H( 8 , 1) 696G NEX T I 6 9 7 0 GOS U B 8 8 3 0 _ - 6980 MO = Z*B*D*0.5 6 9 9 0 RE M *_ : _**_ : **_ : * _ ` _ ` _ : * _ ` _ : _ ` _ `_- * .` _ . _ `_` _ : _ ` _ : _ . _ ` ******_ ` .***_**___ 7000 R EM * C AL C UL A TE COMPBES SO R H P R E Q U I RED [E Q N. 13] * ' 70 20 T 0= M O * 60 06. / 55 0 .*T2*((U5 / P2)**.286-1) 7 0 3 0 R E M _***_ : _**__*___*_ w _*_%-._** .. _*_*****_ ¢c _ * _ _ 7040 REM * C A LCULA T E TOT A L USEFUL WORK [EQN. 1 5 ] * _% 7050 R EM ***_*_*_**_*_ w _*****_ . _*_*_********_ w _*_**********_*_._****_ ` _* 70 6 0 T 3= T6* V / 5 50. , i 7070 REM _ ¢ ***_*_:_*_ . -_*_*****_* ` _***********_***********___-_ i 7 080 REM * CO N V E R T A E ROD YN A M IC T ORQU E T O HOR S E P O WER [ E QN. A I0] * 7 0 90 R EM * A ND T H EN FIND T HE TOTAL H ORS EP O WE R R E QU I R ED [ EQN . 14 ] * I 7 1 00 REM _********_*************_-_******_********_**_********_-_-_ 71 10 T4 = 2.*P 3 *NI*Q6 / 55 0 .

7 12 0 T5ffiT O+ TI + T4 7 130 R EM ***********_***************_**************_ ' _-_.___ 7 1 40 REM * C A LC U LA TE E FF ICI E NCY [ E QN. 16] * !

7 1 50 REM *************************************_*____ J 7 160 B6 = T 3 / T5 I 7 17 0 REM **_ wr ***********_ w _********************_,_ g -_ r _**_,___ 71 8 0 REM * C AL CU L A TE L OCA L M A C H N U M BE R [EQN. A ll] , R E YNOLD ' S N U M BE R * 7 1 9 0 REM * [EQN. AI2 ] , AND D RA G- T O- L I FT RAT IO [E Q N. AI 3] * ,_ 7 200 RE M *_-_************************__*****_-_******___ I 7 210 FOR I=I TO 2 0 7220 Q(O , I )f H (3 , I ) / C2 !

7230 R(I)f H * C ( 3 , I)* D / 2 *H ( 3 , I) / U2 i

i"

b O R I G I NAL PAGE # _ 7240 D ( 4, I) = C ( 2, I) / C (1 , I ) OF POOR Q U A LITY' 72 5 0 N E XT I 7 2 60 R_ 4 __ w _ D E T ERM INE A VAIL ABLE HP A T TH E CURR E NT RP M __ 7 2 7 0 G O SU B 96 4 0 7300 R EM ¢___¢_: * _ . _ r _c_-_ r _ * _-_ - ______ 7 3 1 0 R E M * T H E N E X T SE C TION S A VES DA T A FOR P OST- P R O CESS C R O SS P LOTT ING * 7320 R EM __ * _ *** _ . _ . ___ . _ - _ w o_o w _ . _ - _ w _o_ . __ 7330 I F (T8C5) O R ( A4 =-I) OR ( A 8= O ) T HEN G O T O 7580 734 0 F O R I $=" 00 ## ### . ## ### . ## # ## . ## ### . ## ## ### . # ## . ## #### . ## ## . # ## .

7350 F TE M $= " # _ ' # # . # # ### . #### " 7360 F O R I$=FO RI $+FT E M$ 7370 FOR2$="0 1 ## ### . #### ### . #### ## # . #### ## # . ### # . ### ## #### . ## ,, 7380 FO R 35= " 02 ## # . # # ### . #### ### . #### ##### . # # #### . ### # . ##### ## . ### ,, 7390 FTE M$=" # . ### ## ###### ## . " 7 4 00 FOR 3$=F O R 3$+FTEM$ 741 0 F OR 4 5= "0 3 ## #### . ### # . ## ##### ##### # . # " 7 4 20 PRIN T # 2 % USI N G FO RI $, T8 , A 3 , A 7 , V , _I , H2 / (3.0 4 8 E - 4 ) , T2,P 2 , D , B ,T6, B 6 7 4 3 0 PRINT # 2 % USING F O R2$ , T8 , TO , TI , T5 , Tg , U5 / P2 , T 7 440 FOR I =I TO 20 7 45 0 PR IN Z # 2 Z USIN G FOR3$ , T8 , K ( I ),C( I ,I) , C (2,I),I. / D( 4 , I ), A (I , I),& C (3,1 ) , B(I ) , Q(0 , 1 ) , R( I) 74 60 NE X T I 7 4 70 I F V 4=I TH EN GO T O 7 51 0 7 4 80 FO R I = 1 TO 2 0 7 4 9 0 P R INT # 2 % USIN G FOR4 $ , T8 , H(1,I ) , U( I , I) , H( 2 , I) 7 5 00 N EXT I 7 5 10 PR I NT # 2 % , " 99 99 9999.999 9.9999999 9999.999 " 75 2 0 GOTO 5780 _,_ 7 5 30 R E M * _ *** _ * _-____ **** _ - _o__ . _ - _ r _ c _ 7 54 0 RE M _ ** 7 55 0 REM _-_ FO R MATTED LI N E PRINT E R OUTPUT FOR A LL C A SES _-_ 7 5 60 REM ** ** 7 5 70 RF 2 1 _ * _ * __ ' _ * _"_ ** _ - _ '* _"_ * _ ' ___ wr _ w _ 758 0 A 4 =0 759 0 P RINT # 1 , C H R$(12 % ) ! FO R M FEED " _ 7 6 00 PRINT # 1 , T AB (60 % ) _"RES ULT S FOR C A SE # "| T8 > _ 76 10 IF V4 = l T H EN G OT O 76 40 !N ON - BL OW N C A SE _ .

7620 PRIN T # 1 , T A B(35 % ) _"P R OPE LLE R C H AR A CT ER I S TICS " ;TAB(I O 5 % ) _ & " " J E T CH A R A CTE R ISTICS " 7 630 GOT 0 7 6 50 i 7640 P RI NT # 1 , T A B( 35%) ; "PRO P E LL ER C H AR A CT E RISTICS " i I 7 6 5 0 PRI N T # I 7 660 P RI NT # I , " KSI LI F T COEF D R AG COEF L / D RATIO A L P HA "_ & I "CH ORD / R A D TWIST M A C H N O . REYNOL D S " !

7670 IF V4 = I T H EN 7690 7680 P R I NT # 1 , T A B(1 0 1 % ) !" J E T V E L. M O M . CO E F J ET P R E S ."! I 7 6 90 PRIN_ # I { 7700 FOR I=l T O 2 0 7 71 0 PR INT # 1 USING ' #. _ " _ ' ................... "_ ... , , , , _ . _ . ...... ,,, , . . # # # .# # ### # # # . #### ',& K ( 1 ), C( I, I ). C ( 2,1 ),I l D (4, I ),A(1,I)!

77 20 PRI NT #1 USING ' # . #### ## # # ## . # # # # #. # # #### ## # ##### . # , , & C( 3 , I), B( I) , Q(0 , I) ,R(I ) !

773 0 IF V 4 =I T HE N 77 5 0 Ii II i ii 77 4 0 PRI N T # 1 U S IN G ' # # ## . # ### #. ## ## # ## ## # # . # # f H t ° , & HCI , I ) , U( 1 , I ) , HC2 , I ); 7750 PRI NT # 1 77 6 0 NEX T I 7 77 0 PR I NT #1 7780 PRINT # 1 _ R _ L P_ _ 7790 PR IN T # 1 OF POO R Q _ A L_ 78 0 0 PRI NT # I , TAB ( 3 7 ) ;"O P E R A T I NG CO _ I TI ONS" 7810 PR INT # I 7 820 AS =' VE L= ### . # F / S ENG SPD-- ## . ## R PS ' 7830 B $=' A LT= #### # # . ## F E ET AIR D E M Ur . ###### S L / C b 'T ' 7 8 4 0 C$='T E MP= #### . ## DEG-R A MB PR E S= #### . # PSF' 785 0 DS=A S+ B $+C$ 7 860 PRINT # I 78 7 0 PRINT # 1 US I NG D$ , V , N I ,H2 / (3.0 4 8 E - 4 ) , H , T2 , P2 7880 P R INT # I 7 8 9 0 PR INT # 1, TAB ( 4 0 ) ;"P RO P E LL ER DATA " 7 900 PR INT # 1 79 10 A$ _ ' D I A ffi ## . # FT BLDS=## TH= #### . ## LBS ' 79 20 B$=' E FF = # . #### L A_= ## . ### RQD H P= #### . ## AVL HP= # # ## .# # ' 7930 C$=A$+ B $ 79 4 0 PR I NT # i USI N G C$ , D ,B , T6, B 6, B 2 , TS , T9 7950 IF V4 =l T H E N GOTO 80 4 0 7960 PRI NT # 1 7 97 0 PRINT #1 7 98 0 P RI NT #I , TA B ( 4 2) ;" C O MPR E SS O R " 799 0 PRINT # I 8000 AS =' MASS FL O W= ### . #### S L / S EC COMP HP ffi # ## .# # ## ' 8010 B$='COMPR E SS O R R AT I O= ### . #### ' . , _ ; 8020 C$= A$+B$ i_ 8030 PRINT # 1 U SING C$ , MO , T0,U5 / P2 804 0 PR I NT #1 806 0 RE H _ 80 7 0 REM _ ' _ END OF OU TPUT FOR THE PRES ENT CASE 8080 RE M _ _ F _ .

80 9 0 R. ' _ _ _ " _ 810 0 R E M __ - _ - _ r _-___ r* _ - _ . _ : ___ !

8 1 20 R E M _ SA V E B E TA, B (I ) , AND FIN A L C HO R DS , C(3,I) FOR PROP E LL E RS _ ' _ 81 3 0 R E M _ ' _ A , A' , B , C , C ' , AND D ACCO RD ING T O S C H E M E IN N O TES. ..

81 4 0 RE M ___ ______ 815 0 IF T8 _4 THEN GO T O 828 0

_1_ oF O R I=ITO 20

81 7 0 I f ( T8=I) AND ( V 4= I) T HE N T ( II , I) = C(3,I) 8180 IF (T 8 =l ) AN D ( V 4= O ) TH@ N T(15 , I ) = C (3 , I ) 8 1 90 IF (T8= l ) AND (V 4= 0 ) THEN T( 9 ,I)= B(I )

8200 IF (T 8 = 2) T HEN T (1 2, I ) = C (3 , I )

_ 2 10 I F ( T8 = 2) THEN T(6 , I)=B(Z) 8 220 I F (T8 = 3) A N D (V4 =1 ) T H EN T( 1 3 ,I )= C (3 ,I ) 8230 I F (T8=3) AND (V4 =O) THEN T(i6,I)-C(3,I) 82 40 IF (TS = 3 j A ND (V 4=O ) TH EN T(I O ,Z) =B (I) " 8250 I F (T8=4 ) THEN T (I_ , I ) - C(3,I) !

ORIGINAL PA G E i S

OF POORQUALITY _i

8" / _0 0 I F ( T 8= 4 ) THEN T (8 , I )=B(I) 1 8 2 70 N E XT I | 82 80 I F ( T 7 =O ) O R (V 4 = O) T H EN GO T O 8 32 0 8290 V4=0 8 3 0 0 GOT O 1 7 90 _ 8 310 REM _-_ . ._ . ._ : _' . -_ ' _ : e_ " E XAMIN E NEXT CASE?" DEC I SION POINT _ ' _ : , _ :,:,:,: , : , _ : , _ 8 320 PR INT "ENT E R OP TI O N NUM BER " ; TA B( 3 0); " O = S T OP " i 8 33 0 PR INT T A B( 3 0); "1 = RES TAR T P ROG RAM " 8 340 P R INT T AB ( 3 0); " C ONTRO L -C OR C ONT R O L -Y = EXIT T O MON I TO R " 8350 P R INT "ENTE R OPTION..." ; 8360 INPUT I8 8370 IF I8<=0 THEN STOP 838 0 I F I8>3 TH E N S T OP 8 39 0 G O T O 57O 8 4 00 STO P 8 410 REM _ . . _ . _" t r : _'A' m __ . _' ; .-_ .: . . ___ t: _ P _ P : . : ,__ ; , __ 8420 RE H . " : * ¢ : ¢ " 8 4 30 R EM _ - _ : . CALCULATE LIFT, DRAG, AND DRAG / LIFT PATIO FO R THE NON- 8 440 R EM ._ . ' : B L O WN PROP E LLE R 8 4 50 R h T _ _ : INPT_ £ S" V 3= STARTING LOOP VA LUE ( I - R S T B L AD E ST A TI O N) _ ' 8 4 60 R EM _-_ : _ T(4 , I ) = ALPHA' S _'_ 8 4 70 R EM - m _. A ( 2 , I ) = INTERVAL C ONSTANTS _ i 848 0 R EM _* L( I , I)=LIFT CONSTANTS _ w: 8 49 0 REM _' : _ D(3 , 1)=DRAG CONS T A N TS _' :: 8500 R EM _'_ O U TPUTS'C ( I,I)=LIFT C O E FFICIENT S _-_ 851 0 REM " .. _ C( 2 , I ) = DRAG C OEFFICIENTS _'_ 852 0 R EM _. D ( 4 , I ) =DRAG / LIFT RATIO _ ., _ 85 30 RE M . _ : _ .

8 5 50 FO R I=V3 TO 20 8560 D(3 , 8)=SIN(T(4 , I)) 85 7 0 D(3 , 9 ) =nIN(T(4 , I)) 8580 IF T(4,1 : = 12 THEN FI=6 ELSE FI=7 8590 I_ T( 4 , I ) >!7. THEN GOTO 8 7 2 0 _ " 86 00 RE H 8610 RE M J= RANK IND EX FO R L I F T AND DRAG 8620 R EM 8630 J = INT((T(4 , I)+FI) / 3) 8640 R EM 8650 REM A(3,I)=DELTA ALPHA 8660 R EM 8670 K2=L(I, J +l) 8 6 80 D3 = A(2 , J+I)-A(2, J) 8690 C(I, I)=L(I, J)+((K2-L(I, J)) / D3)_(T(4, I)-A(2 , J)) 87 0 0 C( 2 , I)=D( $ , J)+((D( 3 , J +I)- D (3 , J)) / D3)_(T(4, I)-A(2,J)) 87 1 0 GOT O 8 74 0 B 720 C ( 1 , I )=.O 0 1 8 ; ' 9 C(2,I): S IN(T(4 , I) / Zg) 8750 D ( 4 , I ) : C(2 , I ) / C( 1 , I ) " 8 760 N E X T I [ 8 740 I F ABS( C ( 2, I)) <O .O 00 1 THEN C (2,I)ffi 0 . O00 1 1 ' } 8770 RETURN ] 67 ., % ,,,,, ...... o,o.o _ ,o..m ...... ,°, .... ,-,,oo° ........... °°-= 8780 REM _ ...................................................

8790 R] _ _ r _ 8800 R EM _ SI MP S O N 'S R ULE I NT E GR A T I O N _'_ 88 1 0 R E M _ ' _ _ - k 8820 R E M _ ' _ '.. __ ' ____ ' _ ' _ ' _ ' _ ' _ 88 3 0 Q= O 8 8 4 0 FOR J= l T O 1 0 88 5 0 Q =£ H-Z ( l+2 _( 3 - 1)) 8860 N E XT 3 ORIGINAL PAGE _ 88 7 0 R=O

8880 F OR J =l T O 1 0 0 _ . PO O RQUALI Tt

8890 R=R+Z(2 _ 3 ) 8900 NE XT J 8910 Z=O.05 _ ( 4_ +2 _ R ) / 3 892 0 RETU R N 893 0 R E M __AA__A_AA_A_AA_A_AA_ - _A_AAAAA_A_A 8 9 40 REM _ _ : 8 9 50 R E M _-_ A TM O SPH E RIC CH A R A CTERIST I CS SUBROUTIN E _ - _ 8960 REM _ ' _ 89 7 0 REM ________ 8980 I F H I _I THEN 9070 8990 I F H_20 THEN 9100 9000 IF H2 <3 2 THEN 9130 90 1 0 IF H_4 7 TH EN 916 0 _ : 9020 REM___ , _ AA _ A __ , _ AA _ A _ A __ 9 0 30 RE} { H = DENSITY IN SLUGS / _ 3 9 0 4 0 RE M P2 = A MBIENT PRES SU R E IN L B / _ 2 i_ 9 050 R EM T 2 = A MBI E NT T E MP E R A TURE IN DEGR EE S ' R ' I .

9060 R E M ___ - __A____AA_A_a_ 907 0 P2=2 116.67 92 _ (288. 1 5 / (288. 1 5 -6 .5 _ H2)) _ - _ (-5.2558 7 6) i 9 08 0 T2= ( 28 8.1 5- 6 .5 _H2 ) _ I.8 9090 GOTO 9 1 80 9 1 00 P2= 4 7 2. 7 82 4 8 _ EXP(-O. 1 5 7 6 88 _ (H2- 11 )) 9 110 T2= 3 8 9 . 9 7 i "_ 91 20 GOT() 91 80 _ _ . - 9 130 P2= II4. 37003 _ (2 16 . 65 / ( 21 6 .6 5+(H 2- 2 0 ))) _ 3 4 . 1 63195 _ , 914 0 T2=(2 1 6.65+(H 2 - 20 )) _ I.8 91 50 GOTO 9 1 80 9 1 60 P2= I 8. 1 328 1 2 _ (228. 6 5 / (228.65+2.8 _ ( H2 - 3 2)) _I 2.2 0 11 4 1 9 1 7 0 T2=(288. 6 5+ 2 .S e (H2-32)) _1 .8 9 1 80 H=0.000582 7_ P2 / T2 I 9 1 9 0 RETURN I 9 200 REH _ * _ - ________ i 92 1 0 REM_ ** !

9 22 0 REM _ BL O WN PRO PE LL E R L I NE A RIZ E DLO OK U P SUBROUTINE _ 9230 R E M _ _ _ _ _ I N P U T S _ _ _ _ ** i 9 2 4 0 REM_ V MO M E NTUM C OE FFICIENTS A T ST A TI O N I , U(I , I) ** i - 9 250 REM_ BL A DE A NGL E O F A T TA C K A T ST A TION I , T ( 4 , I) ** 92 _0 REM _ ** 4 9270 R E M _ ___ ; ._o_ - m _ - _-___ _ , . I

g

..... _ . __ , _ . _ _ '' _ r ' _ _ ' 5 _e 1_ . , _ . _ _ _ r

OF P O OR QUALIT Y _ ' 9 2 80 R EM _ L I FT COEFF I C IEN TS A T ST A T I ON I , C( l , I ) ** 9 2 9 0 REM ** DRA G C OEFFICIENTS AT S TATION I , C( 2 , I ) ** 9 3 00 REM _ DRA G/ LIFT C OEFFI C IENTS AT STATI O N I , D(4 , I ) ** _ , 93 1 0 REM _ _ , _ 9320 R E M _ . o _._**_ . . _ , _ o _** . ,___o_-. . e _ . c e e _ , _ m 9 3 3 0 F OR I = l T O 19 _ _ : i 9 34 0 GOSU B 94 70 9350 IF ( T (4, I_ - 1 2 .0 ) AND ( W 2 =I ) TH E N PRINT "I , A O A , UO,U I=";I , T ( 4 , I) , U0 , UI 936 0 IF UO_ = I4 . 0 T HEN G O TO 9 4 00 -_ 9 3 70 C(I , I ) =J ( D 0 , 1 )+J(U 0 , 2) * U(I , I )+U I* (J(U0 , 3)+ J (UO , 4 ) * U( I , I)) _ : 9380 C(2 , I) = J(U0 , 5 )+ J (U O , 6) * U( I , I )+ UI* (J(UO , 7)+J(U 0 , 8) * U( I,I )) 9 390 G OT O 9 4 20 _ 94 00 c(1 , i) =o i , 9410 C(2,1)=SIN(T(4,1) / Z9) 1 9 4 2 0 IF A BS ( C (I , I)_ 0 . 00 1 THE N C (l , l ) = 0 . 00 1 _ _ _ 9430 IF A BS ( C (2 , 1)k 0 . 000 1 THEN C ( 2 , 1 ) = 0 .0 00 1 944 0 D (4 , I) = C(2 , I) I C(1 , I) _ .

9450 NEXT I "_ 9460 RET URN _ J 9 4 7 0 REM*¢ : ***_,_= , -_ _,_ x *= , _**** . ._,_ , ___*************** | 9 48 0 R EM** ** 94 90 R EM** SU B ROU TINE T O C AL CU LAT E L OO KU P TAB L E INTER V AL ** 9 5 00 R EM**, RANK U0 AND A O A F RA CT I O N UI _ 95 10 R EM** _ 9 52 0 .... _"_ ' _ ' _'_'_ ' _ ........... =..............................

953 0 U0=T( 4 , 1)-.0001 9 5 40 IF U O - 1 2 . TH EN 958 0 9550 IF U _I4. 0 TH EN 96 2 0 9560 U0=INT((U0 + I 2) / 3.0) + I.0 9 5 70 G OTO 95 90 9 5 8 0 U0= I 9 590 UI=( T (4 , I)-(3*UO-15)) / 3.0 : ' 9 6 00 I F UO = 9 THEN U I =U I*I.5 _ _ 9620 Ui=O 9 63 0 RETS_N } 964 0 RE M **********.'_********************************************* 96 10 G O TO 96 30 ! _ 9 65 0 RE M _._ _ I 9 660 R EM e , SUBROU T I NE T O C A LCUL ATE AV AI L AB L E H O R SE PO WER ** _I 967 0 RE M ** A S A FU NC T ION O F EN GI NE RP M @ F ULL THRO TTLE =_ 9 6 80 R EM ** ** 1 9690 REM *_=_=_*****_ '¢ **_' ¢ =_' ¢ ***********_*******_*****_***_ ' * _ 9 700 T 9= (-.16 67 )*NI**2 +20 . 8332 *N I - 3 14.99 !

97 1 0 RE_J R N i

I

,I t I .... , , , , , , , • , .L L_ _r _. . . , , : .

ORIGINAL PAGE |4 OF POOR QUA L I TY Symbol C _o ss Re f e r ence Ta b l e The f o ll o wing ta b l e l is t s f o r e a ch pr o gr am s ymb o l " v a ri ab l e n am e ) th_ nu m be r (label ) o f e v e ry stat e m e n t i n w hich t h at s ym bo l can be f ound . S ym bo l s t h at end wit h t he do llar s ig n ( $ ) ar e stri n g v a riabl es , a nd ar e used he r e t o s tor e f o r m atti n g i n f o r ma ti o n for pri n t e r , t e r m i n al , o r d i sk fil e o u t pu t. A ll o t he r s ymbol s ar e used f o r n um De rl c da _ a , wit h no di f f e r en ti a ti on m ade f o r l n t e g e r o r fl oa t in g -po i n t d at a. The Cl ass co l umn con tai ns on ly t he l e tt e r 'I' o r a bl a nk; if a n 'I' i s pr esen t , t he co rr espond i n g S ymbol i s a n array v a ri a b le , ot herw i s e, it i s a scalar v a r i able.

T h e ' R e f e rences ' c ol u mn l is t s t he s t a t emen t la bel s f o r t h o se s t a t e m e n t s i n which e ach s ymbol i s f o u nd. The s t a teme n t lab e l is t he in t e g er po r ti on o f t he R e fer e nc e n u m b er _ t h e fract io na l p o r tio n i nd i ca t e s wh i ch e l e m en t o f t he s t a tem e n t c o n t ains t he sym bol , and i s mo s t o f t e n ' .001 ' indica ti n g t he f i rs t par t . The frac t i o na l p o r tio n wi ll b e ot h e r va l u e s wh e n th e symbol is fo un d i n t he 'I F ...T HEN ...ELS E ... ' t y p e s t a t e m en t , wi t h t he occ u rr a nc e f o u n d aft - r 'THEN' o r 'ELSE ' . The p o und s ig n ( # ) i nd i ca t es t he s t a t ement i n which array var i a bl es are di m e nsi o ned.

S ymbol C l ass R ef ere nc e s A I 9 0.001# 1 7 40.001 1 8 00 . 001 1 8 70.001 1 88 0.001 1 890.00 1 1 900.00 1 1 9 1 0.00 1 1 9 2 0.00 1 1 9 3 0.00 1 19 4 0.00 1 22 10.00 1 24 90.00 1 3 41 0.00 2 472 0.00 1 47 30.001 4 7 90 . 001 5030.001 5120.00 1 51 4 3.001 5210. 00 1 5290.0 0 1 5310 . 001 5 3 10.002 5 3 50 . 00 1 i 5 810.002 7 45 0.001 771 0.001 8 6 80.001 8 69 0.00 1 i 8 7 00,001 A S 78 20.001 78 50.001 791 0. 001 7 9 30.001 8 00 0. 0 01 802 0. 00 1 A1 170 0 . 0 01 17 1 0.001 1 7 40 . 001 I A2 5 9 00.00 1 5910. 001 59 9 0 . 00 1 6 00 0 .00i 6 4 22. 00 2 I A 3 5 90 .0gi 59 20 .00 1 6 00 0 .001 6 010. 0 01 7 4 2 0 . 001 i I A4 5950.0 01 596 0 . 00 1 5 97 0 .0 0 1 612 0. 0 0 1 613 0.001 I 6 140 . _ , 0 1 6290.0 01 63 0 0 .001 63 10. 0 01 7 330.00 1 75 80. 001 i A 5 4 2 90.001 43 0 0.00 1 _ 3 00 .002 4 310.00 1 A 6 6070 . 0 0 1 6080 .0 0 1 616 0 .00 1 617 0 . 001 6 4 24. 0 02 ' _ A7 600.0 0 1 6090 .0 0 1 61 _ . 001 6 1 8 0 . 0 0 1 74 20 . 00 1 ' I A 8 5640.002 564 0 .0 0 3 565 0 .0 0 1 7 330 . 0 01 I !

i

7 0

ORI G INAL PA_ [ _ OE P O OR QUALI T Y _ ' Sym bo l Cl a ss R e fer e n ce s B 7 3 0 . 0 01 1140.001 237 0 . 0 01 2560.001 3390.002 48 7 0.001 4910.001 5510.001 5540.001 6900.001 6980.001 7 420.001 7 940.001 B I 9 0 . 00 1 # 3410.002 3430.002 3450.002 3470.00 2 3490.002 3510.002 3530.002 3550.002 3570.002 36 5 0.001 4720.001 5143.001 5330.001 58 2 0.002 6422.002 6424,002 7 450.001 7 720.001 8190.002 8210.002 8240.002 8260.002 B$ 7 83 0 . 00 1 7 85 0 . 00 1 7 920.001 7 930.001 8010.001 802 0 . 0 01 B1 1240.001 2430.001 3000.001 3040.001 3100.001 3120.001 3210.001 B2 1260.001 2420.001 2 560.001 2580.001 3390.0 0 2 3410.002 4690.001 4710.0 0 1 4870.001 5100.001 i i 7 940.001 i l J_ B3 1280.001 2440.001 3020.001 3040.001 3090.001 _ 312 0 .001 ! _ B5 3040.001 3120.001 3190.001 3210.001 3250.001 , 4 • B6 7160.001 7420.001 7940.001 I B7 760.001 1408.002 1408.003 5_20.001 5860.001 '_ 6422.001

! '

C I 90.001 # 2490.001 3 390.002 3440.002 3460.002 ! i 3480.002 3500.002 3520.002 3540.002 3560.002 !

3580.002 3650.001 3780.001 4910.001 5030.003 5143.001 5510.001 5520.001 5540.001 5550.C01 6430.002 6431.002 6790.001 7230.001 7240.001 ' : _ 7450.001 7 7 10.001 77 20.001 8170.002 8180.002 8200.002 8220.002 8230.002 8250.002 8690.001 8 700 . 00 1 8 720. 00 1 8 7 3 0 .0 0 1 8740. 00 1 8740.002 8 7 50.001 9370.001 9380.001 9400.001 9410.001 9420.001 9420,002 9430.001 9430.002 9440.001 C $ 7 840.001 7 850.001 7 930.001 7940.001 8020.001 d030.O01 CI 140 5 .001 1406.001 140 7 .001 1408.001 1409.001 I 5020.002 5020.003 5030.002 C2 3690.001 3760.001 4060.002 7 220.001 1 C 5 7 5 0 .0 0 1 140 7 .002 140 7 .003 5 810.001 6430.001 , I 6431.001 6502.001 C 6 77 0.001 1409.002 1409.003 6030.001 6424.001 . 7 1 !

• ORI G INA L PA_ I_ _ , OF P OO R QUALI'FC ' _ , b o l C l ass R e f ere nc e s L C 7 7 80.00 1 1 380.00 1 1 390.00 1 1 39 0 .00 2 14 00 .0 01 '-' 1400.002 1420.001 14 3 0 . 001 : ,i C _ 5030 . 002 5030.00 3 5050 . 001 5 060 . 001 C9 5000.00 2 5000.003 5010 . 00 2 5030.001 D 7 00 . 0 0 1 88 0.001 1220.0 0 1 1240.001 1260 . 001 2 3 30 . 001 2400.001 3 210.001 3 78 0 . 001 39 40.001 _ 4140.001 4220.001 43 8 0.001 4570.001 4690.001 , ' F 5510 . 001 554 0. 001 5 62 0. 001 6 59 0 . 001 6 7 90.001 ' 690 0. 001 69 8 0 , 001 7 2 3 0.001 7 420.00 1 7 9 40. 0 01 _ D I 90 . 001 # 20 8 0.0 0 1 2090.001 21 00 . 0 01 2110.001 2120 . 001 21 3 0.001 2140.001 24 9 0.001 2650.001 2820.001 2 8 90.001 7240.001 7 450.001 7 710.001 8 560.00 1 8 5 7 0.001 87 00.001 87 50 . 00 1 9440.001 D $ 78 5 0. 001 7 8 70 . 0 01 _ D3 8680,001 8690.00 1 8 7 0 0 .001 E I 70.001# 256 0. 001 2600.0 0 1 ; F I 7 0.001# 2610. 0 01 26 30 .001 , , I F1 8 5 80. 0 02 85 80 .0 03 86 3 0.001 I F O RI$ 73 40.001 7 3 60 . 0 0 1 7 4 2 0.001 F O R2 $ 7370. 0 01 74 3 0. 0 01 F O R3$ 7 380.001 7 400.001 7 45 0 .001 i_ i FOR4$ 7 410.001 7490.001 FOR S $ 49 5 0.001 5 143 , 001 FTEM$ 73 5 0.001 7360.001 7 3 90.00 1 7400.001 G I 7 0 . 0 0 1 # 263 0 . 001 2 6 5 0 . 0 01 2820.0 01 289 0 . 00 1 339 0 . 00 2 H I 70,001# 3 9 40.001 4060.002 406 0 ,00 3 4 1 00.001 41 5 0.00 1 4230,001 4290,001 4310.001 4 3 80.001 4470.001 4 5 70.001 48 5 0.001 4860.001 5 0 5 0.001 5 060.001 5 480,001 5 490.001 55 10.001 55 20.001 5 5 40,00 1 5 5 50.001 55 60,00 1 6560.00 1 6 750 . 00 1 , i 6 7 60.001 67 9 0,0 0 1 6 8 10.00 1 6 8 20.002 6 83 0.002 i 6840 . 001 69 5 0.001 7220,001 72 3 0.001 7490.00 1 I 77 4 0. 0 01 i

198502164 7 -0 7 5

O RIGINAL P A GEiS

Symb o l Clas s References OF P O OR Q UALIT Y H 1240.001 1280.001 2350.001 3 210.001 3780.001 I 7 2 30.001 7870.001 91 8 0.001 4100.001 4290.001 5510. 0 01 5540. 0 01 6790.001 !

H 2 720,001 940,001 1020.O01 1030.001 2380.001 7420,001 7870,001 8980.001 8990.001 9000.001 9010 , 001 9070,001 9080 , 001 9100.001 9130,001 • 9140.001 9160.001 9170.001 I 2 6 0.001 280.001 300.001 510.001 530.001 550.001 1290,001 1310.001 1320.001 1680.001 1 6 90.001 1730.001 1770.001 1790.001 1800.001 1810.001 2200.001 2210.001 2220,001 2480.001 2490.001 2500.001 2540.001 2560.001 2580.001 2 6 00.001 2610.001 2 6 30.001 2650.001 2 6 60.001 2 6 7 0 .0 0 1 2 6 8 0 .001 2 69 0.001 273 0 . 00 1 275 0 . 0 01 27 6 0 . 0 01 280 0 . 001 282 0 .0 01 28 3 0 . 0 01 2870 . 00 1 28 9 0, 0 0 1 2 900 .00 1 33 70 . 00 1 339 0 . 002 341 0.002 3430.0 02 3440.002 3450.00 2 3460.002 34 7 0.002 348 0 .0G2 3490.002 3500.002 3510.002 35 2 0.002 3530.002 3540.002 3550.002 3560.002 3570.002 3580.002 3590.001 3640.001 3650.001 3660.001 3720.O01 3740.001 3 7 60.001 3 7 80.001 3 7 90.001 3840.001 3850.001 3860.001 3930.001 3940 , 001 3950.001 4210.001 4220.001 4230.001 4290.001 _ 4310,001 4 38 0.001 4390,001 4470.001 4510.001 _ ....

4560.001 45 7 0.001 4580.001 4590.001 4 7 00.001 4 7 10.001 4720.001 4730.001 4740.001 4 8 40.001 4850.001 4860.001 48 7 0.001 4910.001 49 2 0.001 4990.001 5010.OO1 5020.001 5030.001 5030.003 5050.001 5060.001 5070.001 . 508 0 .0 0 1 5100.001 ._ _o_ 5120.001 5140.001 5143.001 5150.001 5200.001 5210.001 5 22 0.001 5270.001 5290.0 0 1 5310.001 _ 5310.002 5330.001 5350.001 5360.001 5470.001 t 5480.001 54 9 0.001 5510.001 5520.001 5540.001 5550.001 5560.001 55 7 0.001 5 8 00.001 5810.002 i 6430.002 6431.002 6440.001 6550.001 6560.001 5820.002 5840.001 639 0 . 0 01 6422.002 6424.002 i 67 9 0.001 6810.001 6820.001 6820.002 6830.001 6570.001 6730.001 6740.001 6750.00! 6 7 60.001 1 6830.002 6840.001 6850.001 6940.001 6950.001 6 960.001 7210.001 72 2 0.001 7230.001 724 0 .0 0 1 7 250.001 7 440.001 7 450.001 7 460.001 7 4 8 0.001 l 7 490.0 0 1 75 0 0. 00 1 77 00 . 0 01 7 710.001 7720 .0 0 1 1 77 4 0.00 1 7760 . 00 1 8 1 60 . 0 0 1 8 1 70.002 8 1 80.002 8 190.0 0 2 8 200.002 8 210.00 2 8220.00 2 8 2 30.002 1 8240.00 2 8 250.00 2 8 2 6 0 .00 2 827 0.001 8 550.001 8560.0 0 1 85 7 0.001 8580.001 8590.001 86 30.001 ' | _690.001 8700. 0 01 8 7 20.001 87 30.001 8 7 40.001 8 740.002 8 7 50.001 87 60.001 9330.001 9350. 0 01 935 0 .002 9 3 70.001 9 3 80.001 9400.001 9410.001 !

94 2 0.001 9420.002 9430.001 9430.002 9440.001 y 9450.001 9530.001 9590.001 .... ,,, _ _ _ r"" - _

y

i

• f . - I S ymb o l C l ass References _ . _ :_ <. . _ ' J 0 _ PO0_ _A L | TY 18 8 360.001 837 0. 001 8380.001 I J 2 7 0 . 00 1 2 8 0.001 2 9 0.001 5 20.001 53 0 . 00 1 !

54 0.00 1 1 730.00 1 1 7 4 0.00 1 1 7 50.0 01 1 7 6 0. 0 0 1 , 177 0.001 86 30.001 8 67 0.001 8 6 80. 00 1 8690.0 0 1 ! 8 7 00 . 00 1 8 840 . 001 88 5 0.001 8 8 60.001 8880.001 I 88 90. 001 8 900 . O01 i !

J I 80 . 00 1 # 280. 00 1 9 3 70.00 1 93 8 0.0C I K 1 7 20.0 0 1 1 7 30.001 K I 80 . 0 01# 1 3 10.001 2 4 90.0 01 25 6 0.001 25 8 0 , 0 01 2 650 . 00 1 2820.00 1 2 890.00 1 34 1 0 .002 3740. 0 0 1 i 3 9 4 0 . 001 4 1 4 0 . 0 01 4 2 20.0 0 1 4 3 8 0.0 0 1 4390.00 1 4570.00 1 4580.00 1 47 1 0.00 1 4870.00 1 49 1 0.00 1 5 1 00.00 1 5540.00 1 7450 . 00 1 77 1 0.00 1 K 2 8670.00 1 8690 .0 0 1 , L I 90 . 0 01 # 199 0 . 0 01 2000. 0 01 201 0 .0 0 1 2 0 20 . 001 20 3 0.001 2040.001 2050.001 2060.001 20 7 0.001 8 6 7 0.00 1 869 0 .0 0 1 : , M 2 7 20.001 300 0 .001 3100.001 M I 80 . 0 0 1 # 2 6 50.001 2 ' 6 8 0. 0 01 2 7 5 0 . 00 1 3760.001 385 0.001 M 0 6980.001 7 020.00 1 8030.00 1 , N 2 7 9 0 . 00 1 3 00 0 .001 3 1 0 0 .00 1 NI 6 9 0 . 001 85 0 .001 12 6 0.001 232 0 . O 01 2 4 00 . 0 01 _ 3 21 0 . 00 1 3 2 3 0.00 1 3 2 50 . 0 01 37 4 0 . O 01 39 40.001 4140. 0 01 4220. 0 01 4 380 .001 4 390 .001 4 5 70.001 45 8 0.001 4690.001 6360.001 7 110.001 7 420.001 7 8 7 0.001 9 7 00.001 N2 6240.001 6250.001 6330.001 6340.O01 6360.001 N 3 610.001 6260.001 6340.001 6350. O 01 0 2 86 0 . 00 1 3020 . 00 1 3090 . 00 1 P 293 0. 00 1 30 2 0 . 00 1 3090 .001 P1 7 40.0 0 1 11 7 0.001 1 28 0.001 2390 .0 0 1 3230 .00 1 I 3290. 00 1 P2 4 100 . 00 1 4 2 9 0,001 702 0 .0 01 7420.00 1 7 4 30 .0 01 I 78 7 0.001 80 3 0 . 001 907 0 . 001 9 1 00 . 00 1 9130. 001 ] 9 1 60. 001 9 1 8 0 . 0 0 1

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r ........... -'r-_ 7........

O F PO _ , . Q UALil_ S ymbol C l a ss R e f e r e nces P3 990.001 I000.001 1240.001 1260.001 1280.001 2 6 10.001 3230.001 32 5 0.001 33 90.002 3740.001 3940.001 4140.001 4220.001 4380.001 4390.001 4570.001 4580.001 4690.001 4 7 20.001 4910.001 " 5210.001 533 0 . 0 01 7110.001 !

| . Q 8830.001 8850.001 8 910 . 001 Q I 70.001# 530.001 6 8 0.001 690.001 7 00 . 001 710.001 7 20.001 730.001 740.001 750 . 001 i 760.001 770.001 780.001 1800.001 7220 . 001 _' 7450.001 7720.001 !

Q6 3210.001 3230.001 3250.001 3280.001 6590.001 7110.001 R 8870.001 8890.001 8910 . 001 R I 70.001# 3 7 80.001 3850.001 7230.001 7450.00 ] 7720.001 R6 1220.001 1280,001 3740.001 4390,001 4580.001 T I 70.001# 2210.001 3430.002 3440.002 3450.002 3510.002 3520.002 3530.002 3540.002 3550.002 3560.002 3570.002 3580 . 002 4730.001 4750.001 4760.0 0 1 4770.001 4780.001 5070.001 5080.001 5100.001 5120.001 5143.001 5210.001 5290.001 34 6 0.002 3470.002 3480.002 3490.002 3500.0 0 2 1 |i 5310.001 5310.002 5330.001 5350.001 5510.001 i 5540.001 8170.002 8180.002 8190.002 8200.002 8210.002 8220.002 8230.002 8240.002 8250.002 8260.002 8560.001 8570.001 8580.001 85 9 0.001 8630.001 8690.001 8700.001 8730.001 9 350.001 9350.002 9410.001 9530.001 9590.001 T 710.001 910.001 1240.001 2340.001 2940.001 3250.001 3300.001 5640.001 5790.001 5900.001 5910. 0 01 6070.001 6080.001 6240.001 6250.001 6430.002 6431.002 7430.001 TO 6630.001 7020.001 7120.001 7430.001 8030.001 . TI 6640.001 6900.001 7120.001 7430.001 T2 3690.001 3710.001 4140.001 4220.001 6810.001 , 7020.001 7420.001 7870.001 9080.001 9110.001 9140,001 9170,001 9180.001 !] T3 7060.001 7160.001 I ' T4 7110.001 7120.001 ' 75

pAGE _ S

o ee OOe T Y

Sym b ol C lass R_fer e nces T4 7110.001 7120.001 l T5 7120.001 7 1 60.001 743U.001 7940.001 i T6 5620.001 5640.001 5790.001 5900.001 5910.001 i 6 070.0 0 1 6 080.001 624 0 .001 6 25 0 .001 6430.002 6431.002 7060.001 7420.001 7940.001 T 7 14 30 . 002 1430.003 1590.001 8280.001 T 8 6 5 0.001 66 0.001 670.001 670.002 680.001 690.001 700.001 710.001 720.001 730.001 7 40.001 750.001 7 60.001 770.001 780.001 790.001 1080.001 1 3 40.001 1580.001 1 8 00.001 2300.001 3 3 90.001 3410.001 34 3 0.001 3440.001 3450.001 34 6 0.001 3470.001 3480.001 3490.001 3 5 00.001 3 5 10.001 3520.001 3530.001 3540.001 3 55 0.001 35 6 0.001 3570.001 3580.001 4060.001 5 6 50.001 6030.001 6200.001 6431.001 6 502.001 7330.001 7420.001 7430.001 7450.001 7490.001 7600.001 8150.001 8170.001 8180.001 8190.001 8200.001 8210.001 8220.001 8230.001 8240.001 8250.001 8260.001 T9 6380.001 7430.001 7940.001 9700.001 U I 80.001 # 4470.001 4710.001 4 7 20.001 4770.001 4850.001 4860.001 4910.001 5 070.001 5 080.001 5 120.001 5143.001 5210.001 5 330.001 5 480.001 5490.001 6790.001 7490.001 7740.001 9370.001 i 9380.001

i

UO 9350.002 9360.001 93 7 0.001 9380.001 9530.001 I• !

9 540.001 95 5 0.001 95 6 0.001 95 80.001 9590.001 9600.001 UI 93 5 0.002 9370.001 9380.001 9590.001 9600.002 • 9620.001 U2 3 710.001 3780.001 7230.001 U4 4140.001 41 5 0.001 4220.001 4230.001 U 5 4150.001 4 2 3 0 . 0 01 681 0 . 00 1 7 020.001 7430.001 8030.001 !

U6 4 8 8 0. 0 01 48 90. 0 0 1 i ,!

b U9 4890. 0 0 1 49 1 0 .00 1 I

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76 _J

O RI G IN A L PA GE [@

OF P O OR QUALIT Y

S y mb ol C lass R e fer enc e s V 6 8 0 .00 1 8 2 0.00 1 124 0.00 1 1 260 . 00 1 1 280.00 1 231 0 . 0 01 2 4 00.00 1 3210.0 01 3 250.00 1 374 0.001 3 9 4 0.00 1 4 380.00 1 4 390.00 1 4 5 7 0.001 4 580.00 1 46 9 0 .00 1 5510 . 00 1 55 4 0 . 001 7 060.00 1 7 4 20.001 7 8 70 . 00 1 V I 9 0.0 0 1 # 37 4 0.0 0 1 3 76 0.001 3780.0 0 1 4 390 .0 01 4 580.00 1 V I 48 70 . 00 1 48 80 . 00 1 505 0.0 0 1 5070 . 00 1 l

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V2 5 06 0. 0 0 1 5 0 80 . 0 01 _

v 3 223 0.0 01 49_ 0.00 1 53 70 . 00 1 855 0 . 0 0 1

v 4 142 0 . 00 2 142 0 . 00 3 1440. 00 1 159 0 . 00 1 219 0 .0 0 1

343 0 . 00 1 345 0.00 1 4 0 6 0 . 00 1 494 0. 0 0 1 5 00 0. 00 1

5 020.00 1 51 4 3.001 53 9 0.00 1 6 030.001 64 2 4 .00 1 '

!

6 4 30.0 0 1 65 0 2.00 1 6 6 80. 0 0 1 7 4 70.001 7 6 10.001 7670.001 773 0.001 795 0 . 001 8170.00 1 81 8 0.001

819 0 . 00 1 822 0 . 00 1 823 0 . 00 1 824 0 . 00 1 8 28 0 .0 0 1

8 29 o . o ol

V 7 4830. 0 01 52 9 0.00 2 5400.001

v 8 15 00 . 00 1 151 0.00 1 151 0.00 2 152 0.00 1 152 0.0 0 2

51 80 . 00 1 53 00.00 1 5 780.00 1

V9 570. 0 01 1440.00 2 22 50.001 316 0 .001 3 2 60. 0 0 1 36 00 . 001 3800.00 1 3880 . 001 W 2 154 0 . 00 1 1550. 00 1 155 0 . 00 2 156 0 . 00 1 156 0.00 2 " 513 9 . 001 6 50 1. 00 1 9 3 50 . 00 1 4 _ X I 70 . 001 # 2 5 8 0 . 00 1 26 30 . 00 1 2 6 50 . 00 1 2750 . 00 1 i 282 0 . 001 2 890 . 00 1 33 9 0 . 00 2 i | Y 2 6 0 0 . 00 1 261 0 . 00 1 I Z I 90 . 001 # 268 0 . 00 1 2 750 . 0 0 1 2 8 2 0 . 00 1 2 890 . 00 1 1 5 5 6 0.001 6 5 60.001 6840.001 6950.001 88 5 0.001 88 9 0.001 Z 272 0 . 001 2 79 0 . 00 1 2 8 6 0 . 001 29 30 . 00 1 5620 . 001 • 6 590.001 6 900.001 69 80.001 8 9 10. 00 1 !

• Z O 3000 . 00 1 3020 . 00 1 30 9 0 . 00 1 3 1 00.00 1 3 1 80 .001 o 3 3 90.00 2 3 41 0 .002 Z 9 I 000 . 00 1 3 4 10 . 002 3 6 5 0 . 001 5 1 4 3 . 001 8 _ 0 . 0 _3 _' .!

941 ooo l i

......... _ ::.:.= , -.._ - - - _-_ ' _ .................

I ; ORIGIN A L p A_I_ ;_ , I OF. POOR QUALITY D e tai led Program Description This s e ction d e scribes in more detail t he pro gr am operati o ns , keyed to the i lin e n u mbers g iven ab o ve. Generalized desc r i ptio ns are pr o vid e d whe r e a

I

i c om bi na t i o n o f the p revi o us de sc r i ptio n and t h e co mm en t s embeded i n th e l ist- i n g ap p ear ade q ua t e ; f or t he l ess ob vi o us functi o ns , m o re de t ai l is p r o v i d e d he r e. T o facili t a t e t he descrip t ion , i t will be ass u med t ha t t he pr o gra m is I memory residen t , ready f or execu t i o n. P r o g r am fl o w for Cas e # I wi ll be !

examin e d t o illus t ra t e opera ti on.

Af t er the array d e clarat io n s t atemen t s a t line n u mbers 7 0 - 9 0 , tw o o u tp u t f il es are o pened and marg i ns a r e define d f o r each (l ines 130 - 1 6 0) . F i l e "0UTPUT.DAT " is used f o r 132 c o_ 'ranprin t er da t a , and " C R PLOT. DA T " i s an 80 c ol u mn f il e us e d f or c ro s s - plot d a t a acc um u l a t i o n in t he o ff-d e si gn p o i nt ana l ysis.

D A T A s t a t emen t s 1 7 0 - 250 c o n t a i n t he 9 X 8 c o effic i en t mat r i x e l e m en t s used i n th e bl o wn pr op e ll er a e rod yn a m i c c o effic i en t look u p t ab le subr o u t ine.

T h e ma t rix its el f , J( 9 , 8 ), is fi ll ed d u r i n g t he e x ecu tio n o f s t a t e m en t s 2 60 - 300 . Th e rows o f J( ) re pr esen t ang le of a tt ac k i n terv a l s of t hr e e degrees ea c h. They s t ar t wi t h the i n terval (- 1 2,-9) degrees a n d e n d w i t h the interval ( 1 2 ,14) de g r ee s . The fi rst f o ur col umn s o f J( ) r ep re s e n t l in e ar ized "_ coefficie n t s u sed in the lif t coef f ici e n t equation a nd the se c ond fo u r co l um n s r e pres en t the coef f i c i en t s fo r the d r ag c o efficient equa t io n . The subro ut i n es a t 9200 - 9630 calcula t e t h e li ft an d d ra g coeff i c ie nts a s a f u nc tio n of angl e * of a tt ack and momentum c oefficien t as ;i C R 'c z - J( '. l) • J( ', 2)C . <J( ', 3) • J (',4) %/ (_ u _ c ¢ _ ( A 1 4 _ _ 1 [, m w i t h C - momentu m coe ffi c ie nt s, i a_ - angle -o£- attack interval lower limi t .!

i _ U " an g le-of - attack i n t erval upper limit

F o r a > 14 degrees, C _ - 0 . 00 ! a n d Cd _ - s i ns . , [

,J #L i i T h e D ATA statements between lines 310 - 5 00 are used to d efine t h e pro g ra m med eases 1 - 19. Each case requires thirty-one data eleme n ts. The data defined here i_ read into a 10 X 31 array Q(10 , 0:30) with statements 5 10 - 5 50 in the order specified by the sy m bols list preeeeding this pr o gram listing.

Program lines 560 - 610 reset certain flags and accumulators specified in the c o mment statements. Lines 620 - 640 starts user interaction by asking for either a predefined case (I - I0) or a signal for manual input (0). If a n o n- zer o ease is e n t ered , airspeed, engine RPH, etc. ar P loaded fr o m t he Q( ) matrix at lines 680 - 7 80; if a zero is entered, t he program interactively o btains the required data at lines 800 - 9 5 0. For the exam p le C as e #I, lines 680 - 780 make V = 270 , N1 = 41.6, D = 6, T = 324 , H2 = I0000, B = 3, Pl = 0, C5 = O , B 7 = I , 0 6 = O , a nd C 7 = 3 . Between li n e s 9 5 0 - 10 7 0 , radian / de g ree !

conversion fa c tors are d e fined and the atmospheric characteris t ics subrou t ine i

)

is invoked. Lines 1090 - 1200 interactivly query for additional case da t &; this informa t ion ha s al r eady been supplied f o r the c ases 1-10, so program flow i j u mps to line 1210 for the C ase #I example.

£he s ec t ion from line 1210 to line 1330 caleuates r un da t a based on the specific case under analysis. Variable descriptions are given in the REMark I s t atemen t s and equation references are also pr o vided t here. As men t i o ned e a r l ier, equati o n referen c es en c losed with a ngle br ac kets <> a re from Re fe r e nc e 4, w hil e th os e en c l o sed w ith squ a re brackets [ L are from t his r epo r t. L ine 1 3 40 b r a n ch e s ar ol,nd the eas e ex a m ina t i o n question at lines 1350 i - 1400, and lines 1420 - 1440 set up the c o ntrol variables V4, T T , and V9 acc o rding to which p ropellers are t o be des i gned / evaluated. For Case #I, both non-blo w n and blown propeller_ will be d e signed ( C 7 = 3); in this situa t ion, V4 = I, T 7 = I, and V9 is lef t at its value o_ 0 defined at line 5 7 0. Fr om the p rogram variable li_t prior to th e program itself; t he c o n t rol variables can b e in t erpreted as (I) the current e ase is non-blown (V4 = I), (2) both non-blown an d b lown pro pelle r s will be ev alua ted (T 7 = I ), a nd ( 3 ) o ut p u t fr o m t h e Anal y tic design se c t io n has not been co m p leted (V9 = 0). When bo t h n o n-bl o w n / bl o wn analysis is co ndu c ted in a single Case, the non-blown evalua t i o n is alwa y s do n e firs t .

Lin es 14 5 0 - 1 57 0 in qui r e as to w hethe r c ert a i n di ag o n i s t ic o u tp u t i s to _t be i nclu de d i n t he p r i n t f il e "0 UT PUT. D AT", an d w he t he r d u rin g t h e ind u ced i v e lo c ity it e r a ti o ns (i nf lo w calc u la tio n s) e er t a ln da t a i s t o be r out ed t o th e user t e rm i n al ( CRT ). Resp o ns e s to t he t wo qu es t io ns cause c o n t r o l v ar i a bles V 8

7 9 _

! and W 2 t o be s e t t o e it he r a 1 (i n cl ude ou t pu t) o r a 0 ( no ou t pu t) . T he I I, se l ectable o u t pu t can ea si l y be loca t ed i n t he listi ng by fir st r e ferri ng to - !

_I t he S ymb o l Cr os s-R e f e r e nc e T ab le jus t a f t er t h e p r o g r am l i s ti n g. In t hi s tab le _I t he con t z o l varia b l e s V8 and W2 can be l o ca t e d , an d all l i n e n u m be r s th a t _ i nclude t h em can b e f o un d.

_! L i ne s 1 5 q0 and 1 59 0 r o u t e p ro g r a m f l o w a rou nd i n t e rac t ive en t ry for b l a de _ , angle of a tt ac k d ist r ib u t io n (l ines 16 00 - 1 7 80 _ if e i the r a d e f i ne d en try I ms " i been ma de , or if a ma nual en t r y n o n - bl ow n / blo wn cas e i_ i n pro g r e ss an d t h e I f i rs t par t (n o n-bl own ) h a s be e n c om ple t ed (V4 = 0) . F o r d efi n ed cases , li n es , 1 7 90 - 18 1 0 load the AOA dis t rib ut ion f rom the Q( ) matrix. L ine s 1820 - 2 14 0 s et up t he a ngle o f a t t ack i n tervals a n d the li n earized co efficien t s f o r th e i li f t and drag c o e f f i c i en t e qua tio ns u sed i n th e n o n- b l own p r o p el l er a e ro dy n ami c I c o eff i c ie n t subr o u ti n e ( l o ca t ed a _ l i nes 8 41 0 - 8 7 7 0 ). Th e equa tions r e al ize d I i i n t h is su bro u t ine are s i mil ar to th os e us e d _ n t h e bl own pr o pel l er l o o k u p I t abl e, an d can readil y be dete r m i ne d by i n s p e c t ion of t h e c ode. i : At l i n e 2 190 , p r ogr am f lo w i s d i ver t ed to l i n e 2540 f o r t h e blo wn _ : p ro p el l er e xami na t io n . F or t h e e x am p le Cas e # I, t h e n o n-bl o w n pr o pel l er i s _ f i rs t d esig n ed so f lo w con t i n u e s t c li n e s 22 00 - 2 24 0 w h er e t he non - b lown °, pr ope ll er a e r o d ynami c c o eff i c ie n t s a re o b t ained. B o th a na l ytic an d s t r i p I " i n teg ra tio n de_ig n i s ef fe c ted f o r t h e n o n -- bl own pr o pell er_ i f the a n al y t i c i

I

desig n ha s b e en co m pl e t ed ( V9 = I ) , l i n e 22 50 r o u t e s ex ecu tio n to l i n e 2 5 4 0 to avo id t he f i rs t se t o f a na l y t i c _ ' __ _ nt er o utput ( l i n e s 22 7 0 - - 2 53 0). Be n wee n , li n e s 25 4 0 and 3 1 20 , t h e an a l y t i c al d e s ig n i s m ad e bas ed on e q ua t io ns l i s t ed i n li_ t he RE M ar k s t a te m en t s. Thi s des i gn i s ca rri e d o ut f or bot h anal yti c _ n d s_ r ip i n teg ra tion eval u a t i o n s i nce s o m e o f t he r e s u lts o b t a i ne d i n t he an aly t ic I_ calcula t io ns are us e d la t er by t he str i p i nt e g r a t ion s ec t i o n . Li n es 31 20 - 33 00 sen d mo r e an aly t i c o u t p u t to the p rint er ; c o n t r ol s t a temen t s at li n es 3 ]. 60 and 3 260 ro u t e flow aro un d P R I NT s t a t e me n t s if t h e a n a l yti r ou t p ut is c o mpl ete.

Li ne s 33 70 - 34 1 0 do t h e ana l y t ic c hord a nd b e t a d i stri bu tio n c al c natl on s for al l ca se s I , 2 , 3 , or 4. L i ne s 3 4 3 0 - 359 0 sa v e o r re sto re t he s e chord and be t a d ls_ r ib u tlo n s f or la t er ca s e u s e. F o r t he examp l e Ca s e # 1 , l in e 3 4 3 0 sa e e s t L e be t a d lstr lbu t lo ,As i n t he 5 t h co l, a n n of t he T ( ) arra y i f t h e n on - blown propelle r i s be ing a na lyzed _¢4 _ - 1) . For C a s e #2 ( i , .° - _ 3 _0 ), t he 'i chord d i s t r i bu ti on s used a r e ob t ained fr om thn 15 th col um n of t he T ( _ array , i ' wh i ch wa s s aved a t l l ne 8180 dur i ng a Case # I blo wn p r opeller de sig n rim. TI- _ it

.o

1 r

L - cu rr e nt schem e f o r s a vi n g a n d r e storing d at a can b e s e e n i n t he acc o mpa nyi n g t a bl e ; data is s tored / read i n t h e vicinity o f lines 3 430 - 3 590 o r 8 1 60 - 8 270 . i The rationale for t h is pla c ement is that t h e 3400 lo c ations o ccu r b e f o r e an y strip integration c al c ulations take place t h at are impa c ted by the chord or : !

beta distributions, an d t h at t he 8100 lo c ations o cc ur after all strip i n t e g- ration c a lculations h ave t a ken pl a ce a nd t h e da ta can be used by l a ter cases. 4 C ase # Bl o wn ? A c tion @3400's Action @8100's

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I no T(5,1)=Beta T(ll , l)=Chord 2 yes C ho rds=T(15,1) T(12,1)=Chord, T(6 , 1)=Beta il I yes none T(15,1)=Chord, T(9,1_ = Beta : i 3 no T ( 7,1)=Beta T(1 3 , 1)=Chord i - t 3 yes no n e T(16 , 1)=Chord, T(10,1)=Beta d ' 4 yes C ho rds = T(16 , 1) T(14,1)=Chord , T(8 , 1)=Beta 5 yes Beta=T(9,1), Chords=T(15,1) none I I 6 yes Beta=T(6,1), Chords=T(12,1) none • 7 yes Beta=T(10,1),Chords=T(16,1) none • 8 yes Beta=T(8,1), Ch o rds=T(14,1) r ) ne _ 9 no Beta=T(5 , 1), Ch o rds=T(ll,l) none . I0 n o B e ta=T(7,1), Chords=T(13.1) none _ Q

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_describ_d in t h e REMark statements) and the last of the analytic print • ii Lines 3600 - 3860 consists of the rest of the analytic calculations i state z _ents. C o ntrol statements at 3600 and 3800 route flow around these _I outp u t statements if the an alyti c o ut p u f o r _his ca se h a s a lre a dy bee n d one.

_| State m ent 38 8 0 sets toe control variable V9 = I to i n dicate the analy t ic il ou tp u t h as been completed f o r this example Case #I.

Lines 3890 - 5620 implement th e strip integration equations con t ained in _ i !] t he mai n part o f this report or ( for the induced velocity iteraZions) in this . , appendix. Details f o u n d in th e REMark statements should prove ample to follow i the program flow through this section. Two area s will be expanded here fo r | clarity. First, ac line 4060 is the m echanism to have either a blown or a E * _I non-blown pr o peller. If t h e cas_ ' i d entification is i, 2 , 3, o r 4, and if t h e propel l er un d er ev a lu a tion is bl o wn _ V 4 = 0), the n the jet velo c i t y a t t h e tip

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' | (station 1 9 ) is s e t t o 95 % of the speed o f s ound ; ot h erwise, the jet v el oc i t y i s s et to J and _he propeller i s non-blown.

Secondly. if the propeller i s blown, it is blown f r om roo t to tip ( s tation I to s tation 19). I f pa r tia l span blowin_ is desi r ed, then c oding c hange s in 8] I t h i s sec ti on ar e n ece ssary t o (I ) r ed u ce t he la s t b la de stati o n number at w h i ch blo w in g will o cc ur, a n d 42) mat ch the lift c oeffi c i en t at t he tra ns ition be t we en t he blown and n o n -b l own b l ad e s e c tio n s. T he follo w i n g c od e replac e men t c ould be u s ed as a basis for a partial span e valuation, with the i . lner 2 / 3 (r o o t t o station 14) blown, and t he outer 1 / 3 (station 15 to 20) n o n- . blown.

R e p l ace m en t Code for Evalu a tio n o f P a rti a l S pa n Bl o wi n g 396 0 REM*-_'******' : r_**'_ , '*'._ , ,_'_J_* * ****'-'*'x'-' * _ -....... _ w.: *** 3 97 0 RE I d _ _ - _ 3 98 0 R EM** ROU TE P R O GRAM FL O W B AS ED O N B L O WN O R NO N-B LO WN O PTI O N *_ 3 99 0 R EM** ( BLOWN, V 4=0; N O N- B L O WN, V 4=I) ** 4 000 IF V4 = I TH EN G O TO 4 67 0 4010 R _ ' M** ** 40 20 REM ************ .. _**_ ' ,_* - _**_**********__*_-_*****_* 4 030 R EM . ****_'_** D ETERMINE MOMENTUM COEFFICIENTS AT STATI O N 14 **_-_*_*** 4 0 40 R EM_ N E C E SSARY T O MATC H LIFT O F S / C AI R F O IL _.._-_e***** 40 50 REM 4060 I=14 4 070 GOS U B 9 4 70 40 80 U3= ( C ( I , 14)-U(UO, I)- UI * U (U0 , 3 )) / ( U( U 0 , 2 ) +UI *U(U0 , 4)) } 4 0 90 R EM 4100 R EM_._-'_*_',_**** U 3 I S T H E M O MENTUM C OE FF ICI ENT A T S TATION 14 _-"_" - _ , " ' 4110 RE M 4120 REM* ' _ ' '_._'_'_ ' w'_'_ NOW C A LCU LATE T H E J E T V E LOC ITY AT STATION 14 ..... • .......

413 0 R EM i 4140 H(I , 14 ) =V (14)'26.4"U3"*. 5 } 4150 RE M 41 60 REM******_,_** TH E REQUIR E D J ET P R E SS URE AT S TAT IO N 14 IS _-_****e_, i 4170 REM !

4180 H(2 , 14)=0. 5 *H_H(I , 14)*'2. +P 2 { 4 1 90 R EM , 420 0 R EM .... _ , . _ .... TH E H UB PR E SS URE TO GiVE TH IS S TATI O N 14 I S _ , _*._ , _._** .r : 421 0 REM i 42 2 0 U 4 = ((PI*NI*K(14),'_D ) **2) / ( 3 4 3 2_T2) _ ", 42 3 0 U S = H(2,14) / EXP(U4) 4240 R EM REM**_**_.. , . • • IF REQU I RED HUB P RE S S U RE IS LES S T H AN STATI C ************ { 426 0 R EM_***Y . _ : P RE SS [_E, US E S T A T I C P R E SS URE AT HUB! *._*** . _o_*** I 4 2 7 0 R EM I 42 8 0 I F (US _ P 2) AND ( C 6_ _I ) '[ T H EN P R INT " RE Q U IRED HUB PRES S URE IS L E S S THAN S TATI C FOR CAS E #";T 8 I 42 9 0 IF (US <= P2) AND ( C 6 < > I) THEN NI = NI*(T / T 6 )**.5 4 300 I F U 5 < P 2 T H EN U5= P 2 4 3 10 REM I 4 330 R FM* C AL CUL AT E J ET PR E S SURE AT EA C H B L ADE _TATI u N [E Q N. 6 ] 4 3 40 RLI w*** w *****_***w**w****_****_**w*_._*** w *****_*_ *.**._Yo_ .' : -_*_._-_- t _-_o_*** : 435 0 REM 4 36 0 ' O R I= I T O 14 I J ORIGINAL PAGE i _ 4370 U4f ((PI* N I* K (I)*D)_ ' : 2 ) / (34 32 " T2) O F P OOR QUA LI T Y ' : 43 8 0 H (2 , I )= US* E X P( U4 ) 439 0 R E M 44 00 _r._ ..............................................................................................

441 0 R EM * C A LCUL A TEJET VELOCITY A T E A C H S TAT I O N A LSO [EQN. 2] 443 0 RE M 4440 H(1 , I) =( (( H( 2 , I )- P 2) ' 2) / H) "_ :' " • 5 445 0 RE M 4460 nmm.............................................................................................................

447 0 RE M* * 44 80 RE M* CALC U LATEEACH B LADE ST A TI O NS LOCAL V ELOCI T Y [ EQ N , 7] * 4490 R_M* * _ r,u.,. . . _ ,. _ ..- _ . ._ . _ . _ ' . .-' - -' _ _ _ . . , , _ ,. . , , . .,. , . , . _ .. . , ... _ , . _ , . ., , ., _ , _ a _ , , _ , , _ , , ., ., , , .-,..,., , , , ._ .. _ ..,.. ,. _ . ., ., : _ ., _ . ) .. . _, o .,° _ . ,o. #. . A °. _ ° !

4497 H(3 , I) = (V . . _2 + (PI . . K(I ) . . D . . NI) .... 2) .... .5 44 98 V(I )=SQR(V** 2 +( 2 *PI*K( I ) *Rd*NI )** 2 ) 44 99 REM 4500 R E M _-A._ . _'_-_ rf _ ¢ _ . _ . _¢_¢_ * _ : _ : _.__%_-_°_¢_ : _-_¢_ 4501 REM* . .. AND F I NA LL Y , C A L C UL ATE THE MOMENTUM COE FF ICIENT 45 0 2 R E M* AT E A C H BLAD E STATIO N [ E QN. I] 450 3 REM .......... _ '" " _ ..................................................................................... * _ 4504 REM 'i "_ 4505 REM ! i_ 45 0 6 U (1 , I) = ((H(1 , I) / H(3 , I))*' 2 ) / 696 .2 RE M .,. _ .. _ .,. _ . _ . ._ . w . . , . __ ,_ _ . , . . ........ . ,. _ . _ . .w . . , . ., . .,..,. . ,..,. . ,. _ . . , . . ,. . ,.., ............. . ,.. , . _ ..,. . ,..,. _ .. , .. w .. w . . , ..,. . ,o _ . ......... .,. .. ,..,. ** . _ : _ t. . 450 7 ........................................................................................................................... !

450 8 REM* END O F L O O P ' : 4509 REM i 4510 N E XT I O th e r c h a nges m a y b e require d to th e p ro g r am d e p ending o n th e m e th o d used _

i

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to mat c h developed thrust to required thrust. For example , if the momentum _ coefficien t s are s c aled t o ac hieve the required t hrus t , then program flow af t er j et a dj u s tment m us t re t urn to sta t ement 4120 t o re ca l c ul a te the r e q uired h u b i press u re a n d othe r a f f e c t e d qu a ntities. In a ddition , the b lown p ro p ell e r ._ aerodynamic coeffi c ient subrou t ine must be modified at line 9330 to ac c oun t for the p a r t ial spa n blowing t o sta t i o n 14. C a lls to the n on-blown propeller aer_ i c o e fficien t rou t ine mu st set V3 to s t a t ion 15, the firs t n o n- b l o wn l oc a t i o n.

Lines 5630 - 6510 test the develo p ed t hrus t against the require d thrust , a n d i f t h ey d o n o t m a t c h w ithin 1% o f the required thrust , s o me f o rm o f _ , ad j us t m e n t i s implemented. Th e sp ec ifi c form of a dj u stmen t employed w a s di sc u ss e d earlier, in t he Ca s e Table Iden t ifi c a t ion of Table AI. For t his progr a m, Alph a , Be t a , engine s peed, or c hord s ca ling is u sed to ob t ain the _ ! .

r equ ir ed valu e s o f t h r us t , wi t h the sp e c i f i c pa r a me t er c o nt ro l l e d by the v a lue s o f B7, C5 , C 6 , o r C a s e # . For the n on-blown p ro p eller o f exam pl e Ca s e # I, the ch o r d s a _ e sca l e d a t li n e n u mb er 64 3 0 , b e cau s e ( I ) B 7 = 1 caus e s pr o gram fl o w % , " i : " | ; ; to sk ip t h e B eta a dj us tm en t ( line 5 860 ) , (2) V 4 = 1 ca u s e s a s kip of t h e Alp ha + a d j u stment ( l i n e 6 03 0 ) , ( 3 ) Case #I (T8 = I) cause s a skip o f t he eng in e s p e e d adj u st m e n t ( li ne 6 200 ) , and ( 4 ) C5 <> 1 a n d Case # < 5 r e s u lt s in t he ex e c u tio n ._ o f l in e 6 4 30 , whic h i s t he chord adjus tm en t . Si m il ar logi c can b e a pp l i ed to v e r i fy th_ f o rm empl o yed b y ot her cases. A f t er any a d j u s t m en t is m a d e , p r og ram f lo w re t urn s to l in e 4 5 60 to reca l cu l a te t he induc e d v e lo c it y c ompo nen t . Th i s ite r a t iv e p r o cess o cc u rs un ti l e it he r a sa ti sfac to ry t h r us t mat ch has bee n o bt a i ned , o r t h e us er te r m i na t es t h e case e va l u atio n .

L i nes 6 520 - 72 9 0 c alcu l a t e t orque, a ir mass f low , c o mpress o r p o wer r e q u i r e ments , et c. This sec t i o n has am p l e c o m m e n ts to f o ll o w t he ope ra tio ns • wi t h references as app ro pr ia te . Line 7 2 7 0 ca ll s a su b r o uti ne t o dete rmi ne th e h ors e p o w e r avai l able a t a s pe c i f i c e n gi ne s p eed and full t h rottle f or a t Tur bo e ha rged e ng ine of 520 i n 3 d is plac e m e n t .

Lin e s 730 0 - 75 20 o u t p u t cr os s- pl o t d ata to th e "C RP L O T .DAT" f i le f or th e o ff- d e si g n cases ( 5 - 1 0). Each time a thr us t adjus tm en t is mad e in t he off - desi g n ru n s, th e crossp lot da t a fil e h as da t a added to it. In th is fashi o n , d a t a i s acc um ula t ed as a funct io n o f t he p ara met er m a k in g the t hr u s t : a djus tm en t. Th i s da t a i s t hen u sed to g ene r a te pl ot s li ke Fig ure 4 i n t he ma in i re po r t . The varia b les seen in l ines 7 42 0, 7 4 J 0 , 7 4 5 0 , and 7 4 90 are saved at -' each da t a p o int ; the i n t erpreta tion of these va ri a bl es can be ma de b y r efer ri n g i - t o the Li st of Symbol s lo cated jus t befo re t h e prog ra m l i s t ing. Th e r e a r e f o u r 1 r e c o r d type s ou t p ut t o t h i s f i l e; t he rec o r d typ e id e n t i f i ca tio n i s a l w ay s t he fi r st t w o - digit n um be r i n eac h r eco r d . Vali d rec o rd type s a re 00 , 01 , 02 , 0 3 , and 9 9 . R e c ord t y pe 99 i s a d ata poi n t de l i m ite r . Da t a ana l ysis o f the c r o ss - _ plo t f ile requ i res a k n o wl edg e o f t he o u t p u t f or ma t; t he eas i es t way t o obt a i n t hat i nf orm a tio n i s t o run t he p r og r am an d then ty pe (p art o f ) the c ro ss- plot f il e. W hen d a t a i s a dd ed to th i s fil e , n o p r i nter f il e o ut p u t i s g en e rated.

This act io n i s c o n t rol led by th e v ar i a b le A4 , a s ca n be seen in li ne s 733 0 an d 7 52 0.

Lin e s 7 530 - 81 00 o u t put p rinter d a t a f or t he stri p in t e g r ati o n e q u a tio n s .

The p rin t er file i s cur r e n t l y s e t up fo r a 1 32 c o l u mn printer and essentially all c o l u mn s are r e q uir e d f o r t he b l o wn p r op eller o u tpu t q u antities. F e wer a r e ne ed e d f o r the n o n- bl own p r op e l l er o u t pu t, b u t an 80 colum n p r inte r is sti ll n o t a d equat e . C o n trol va r ia bl e V1 i s use d to select the co rr ect o u tpu t statemen t s (non -b lown / b l o m O .

L i nes 811 0 - 82 70 save final chord and b e t a values as was d i scussed earlier. Lines 8280 - 8300 con t rol t he pro g ra m flow for t he m ul ti ple _ L e v a l ua tion c as e s, s u c h a s the e x a mpl e Ca s e # I . T h is c a s e fir s t r e q u ir e s t he a n a lytic de s ign of a non-blown propeller, followed by the strip integration d e sign of th e s a m e n on-blown prop e ll e r. After a' output is c omplet e (lin e 8 100), and th e chord values hav e been saved, statement 8 2 90 sets c ontrol variabl e V4 (w h ich w a s i for the non-blown propeller) to a 0 (for a blown prop e ll e r d e sign). Control then r e turns to st a tement 1 7 90 to design / ev a lu a te the blown prop e ll e r. W h en e xe c ution returns t o statement 8 2 8 0 , V 4 = 0 ca us e s th e program flow to resume at line 8 3 20.

Lin e s 83 20 - 8400 execute a t the end of e ac h case evaluation a nd allow the us e r to run a nother ca se or to stop the program. If a_other ca s e is sele c ted, c ontlol returns to line 570_ otherwise the program stops a t line i 84 0 0.

+ M o st o f t he s u broutines f ou n d b e tween lines 8410 and 9710 have already be e n d is c ussed. Th e one ex c eption to t h is is t h e Simpson's Rule num e ri c al integr a tio- subroutine foun d a t 8 7 80 - 8920. T h is routine ha s t h e integrand passed to it in t h e Z( ) ve c tor w h i c h h a s 20 elements. Lines 7 4 8 0 to 7 5 00 sum the odd numbered Z( ) elements into t h e temporary vari a ble Q, th a t is Q = Z(1)+Z(3)+Z(5)+Z( 7 )+Z(9)+Z(ll)+Z(13)+Z(1 5 )+Z(1 7 )+Z(19) a nd lines 7 5 20 - 7 5 40 sum the e_en numbered Z( ) elements into t h e tempor a ry v a ri a ble R, a s R = Z(2)+Z(4)+Z(6)+Z(8)+Z(10)+Z(12)+Z(14)+Z(16)+Z(18)+Z(20) These qu a ntiti e s a r e t h en forme d into the integr a l by a ppli ca tion of g = 0.05 (4Q + 2R) / 3 (where Z is a sc a lar) The integr a l is returned to the calling program in the scalar variable Z. _ . _ Suggestions for Tailoring the Program _ l T o st a rt a new effort using t h is progr a m r e quires modifi ca tion of two m a in program elements: (I) the airfoil and engine ch a r ac teristi c s, a nd (2 ) the pre- defined ca se identificati o n, a nd program logi c flow. T he ca se i d entifi ca tion a nd progr a m fl o w h a ve been dis c ussed e a rlier. The rem a ining c h a nges a r e dis c u s s e d h ere.

T h e m a in t a sk in ada pting t h is progr a m to use some _rbitr a ry a ir f oil s hap e a nd engin e c h a r ac teristi c is to obt a in t h e pie c ewis e -line a r c oeffi c ients use d by the l oo kup table su br o utines (Lines 8410 - 8770 , 9200 - 9630 , and 9640 - 9710). This data is obtained from airfoil lift / drag polars by first srgmenting the lift / drag curve into three degree parts (for the current program), and then 'i obt a ini n g c o e ffi c ie n ts for the slope - i n ter c ept form of a str a ight line best i . Z" . _ ' = _,,_. _ ' i I -_' i ' ?

'i rep r ese n t i ng the li ft / dr ag curve over e a c h an g l e of a tt a ck r a nge. T his d a t a is i ' then _tor e d in the DAT A stat e m en t s ( 17 0 - 2 5 0 ) use d to l o a d the J ( ) arr ay for / i t he blown p r ope l le r , or i n stat e m e nts 1990 - 2140 for th e n o n - bl o wn p r ope ll e r.

E n gine c ha r ac teri s ti cs a r e d eri v ed i n a si m il a r manner , an d the s lo pe- intercept J : da t a us ed in statement 9 7 00 f o r t he h o rs e power available subroutin e .

T he re ma ining c o m m e nts a re i n tended to as s ist in t h e c on ve rsion of this program to run on s ome other m a c hine. Sin c e it is impossibl e to c on s ider a ll impl e m e ntations of BASI C that might be e n c ounter e d, the stat eme nts t ha t app ea r h t o b e non- sta n dard ar e d is cu ss e d. Esta b lis h ing n e w c as e s f o r ev aluation, "- " | _i m o difi c ation o f t he t h rust mat c hing p r oced ur e t o a ccou nt f o r o t he r pa ram e tri c va ri a tio n , r educ i n g t he b lo w ing span , an d ch a n ging t he eng in e cha r ac t er i s ti cs !

h a ve a ll been d is c u s s ed .

Lin e s 7 0 - 9 0 will c a u se p r o blems w it h t h os e ve rsions of _ A S IC t ha t do n ot

i '

al lo w mul t i ply subsc ript ed ar r ays . T h is pos es a ve ry diffi c u l t p robl em , and : most l ike l y, ma k e s t he p rogr a m un u s a ble. Port una tely, n ot many ve rs io ns hav e : files. A printer disk file as such may no t be r equired; if n ot, the n re p lac e i s u ch li m it a tio ns . Li n e s 1 3 0 - 1 60 may cause pro blem s in the for m us ed to op en i line 130 with t h e a pp ropriate type. The MARGIN statemen t may not be all o wed ; q_ iJ d el e te it , o r find a suitable replacement to tell,the computer how wide the I lo n gest li n e w i ll be in e ac h file. % i L i ne 6 2 0 pr i n t s t h e c ur r ent d a te on the us er' s termi na l; it can e as i l y be ' removed if the function is not otherwise available. The majority of the i prog r am is "standard" BASI C , so the next possible problem area are in the j- ou t pu t s e c tio ns sca ttered th rou gho u t t h e pr o gr a m. To a la rge exte n t, the PRI NT - _ USIN G s t a tement w as u ti l ized to more pre c i s ely control the outp u t form a t. If t h e selec te d v e r s ion of BA S IC has a P R I NT US I N G s tatem en t , it m ay n ot a gr e e J exa c tly with the one u s e d in the c urrent p r ogram, b ut o n ly s ma l l c hange s s h o u ld be require d . If no PRINT USIN G i s availa b le, t hen all s tri p int eg ra t ion out p ut wil l have to be r ed o ne to fit whateve r PRINT s t a t eme n ts are av a ilable. The format va r iable nam es u s ed ( e .g. FORI$) may al s o be a pre b l em; if s o , c hang e t h e name s . String c on c atanati o n i s u s ed c o a c hieve lo n g format stri n gs (lo n ge r t ha n 30 c ha r a c t ers) a s c an be s een in l i ne s 7 360 a nd 7400. If thi s c annot b e acc ompli s h e d in thi s manne r , some o t he r s cheme m u s_ b e de vised.

I t i s li ke ly t h a t the p ro g r a m size w i ll c a us e d i ff i cul ti e s in t ran s f e rrin g , _ _I t h i s pr o g r a m to an ot h er m ach ine. Si n ce t he m achin e u sed f o r the c u rren t s t u dy I ] com pi l , _d t he B ASIC so u rc e p ro gra m to i t s o wn machin e c o de , and use d c ommo n 86 ': mem o r y r es iden t r u n-ti m e l i b rari es , the actual n u m b e r o f b yt es o f mem o ry r equi red f o r i n t e rpre t a ti ve mach i ne execu tio n is n ot known. Ob v iou s techn i ques t o re d uce m em ory re q u i re m en t s i nc l ude ( I ) re mo va l o f t he R EMark s t atemen t s and t he c omment s o n ea ch l ine , and (2) seg men t a tio n or cha i n o p e ra tio n o f the + pr og ra m . In an i nterpre t a tiv e B ASIC c o mp ut er , R EM a r k s t a teme n t s r e q u i r e a v a i la ble use r memory just a s ex ec utable stat e men t s do, but th e y do not affe c t prog ra m re s ults. If s e gmentation o r c h a in opera t ion is us e d, t h e progr a m ca n be divi de d into p ar ts in a f ash ion simil a r to t he w a y t h e pr o gr a m w a s d is c u ssed in t h e G e n e r a l D e s c ription portion of this appendix.

J Con cluding Remarks A c om p r ehe n s iv e dis c ussion of t h e propeller design program used in th e c urr e n t study has b e en giv e n. Th is dis c ussion first addressed the gener a l cha r ac t e risti c s of e ac h m a jor progr a m se c tion, a nd th en d e sc ribed in det a il t h e mann e r in whi c h predefined ca ses here set up. A c omplet e program variable + list, with t h e e ngine e ring units used by th e progr a m ( a s a ppropriate), w a s giv e n just prior to a c omplet e prog ra m listing. A symbol ta ble (prog ra m v a ri a ble) c ross-refe re n c e listing was t h en giv e n to f ac ilit a te progr a m und e rstanding. A d et a iled program w a lk-t h roug h followed th e s e list i ngs, keyed to t h e progr a m lin e numbers, a nd using a n e x a mple ca se for clarity. The a ppe n dix ends with some c o m me n ts o,l a d a pting t h e progr am to so m e a rbrit a ry i a i r foi l an d engi n e c h a r ac teristi c a nd tr a nsfer r i n g the progr a m to ot h er I { machi n es.

R EFE R ENCE S .¢ 1. Br aslo w , Al be r t L.# A erodynam i c Evaluat i on o f C i rculat i on Con tr ol Pr opellers. N A SA C R - 16574 8, J une, 1981.

2 . Fly i n g , A nnual and B uyer's Gu i de , 1980 , Aircraft D ir ec to ry, pp 7 0 - 93.

3. En g ler, Ro bert J. : L o w- Spe ed Aer o d ynami c Charac t er i s ti cs of a S ma l l , F i xed-Tra i l i n g -Ed g e C ir cu l at io n C o n t r ol Win g C o nf ig ura ti on F itt ed to a S upercr i t i cal A i rf oi l. David W . Tayl o r Sh i p R esearch and Deve l op m en t Cen t e r / AS ED -81 , March , 1 98 1 .

l 4 . Larra be e , E. E u g ene : P rac ti cal Desi g ns o f M i n i mum In d uced L o ss P ropelle r s. : SA E Technical P a per 790 58 5 , A pr i l, 19 7 9 .

5. Larra be e, E . E u g en e, De sig n o f Pr o pel l ers f or M oto rs o are r s. Sc i ence and Techn o logy o f Low Spee d and Mo tor less Fl ig h t , N A SA C P - 20 85. P r o ceedin g s i o f a S ymp o s i u m held a t NAS A -La ng le y , H am p to n, V A , March 2 9-3 0 , 19 7 9.

6. U . S. St andard A t m os phere , 1962 , N AS A , U. S . Ai r F o rce, a n d U. S . Weather B ureau, December, 196 2 .

1. Rq _ ort No. 2. Governn _ ntAccom on No. 3. R ac ipient ' sCatalo g No.

NASA CR- 1 6 5 96 8 4 . Tit* _ a nd Subtitle 5 . R _ p or t O e ta Circulation ControlPropellers for GeneralAviation, A p ril 1983 Incl udin g a B A S ICC o mputerPr og ram s . I Nw f orm l ng O r pn izatio n ,m 7 . Autho r (s) 8 . Perf ormi ng Org an l ut ion Rep _ No.

I.Taback, A. L. Braslow,A. J. Butterfield 10 . W or k Unit No.

9 . Performing Organization N a me a nd Addrm The Bi on etics C o rp o ration , . Contract or Grant N o .

20 ResearchDrive NASI- 16978 H a mntnn _ V ir n i n i_ ? _ i_RR 13. TyI _ of Report andPeriodCover ed 1 2 . s p ons _ , in g _e r _ y _ , me an d A ddr m C on tractor [ ,ep o rt NationalAeronautics and SpaceAdmi nistration 14 . S p on s oring A ge n c y Washington, D. C. 20546 15 . S ,Jl _ em an m'y Not** LangleyRe se archCenterTechnical Monitor Ge o rgeMaddrea 18 . Abstract This studyevaluated the feasibility of replacingvariable-pitch propeller mechanisms with circulation-control (Coan a d_ effect)propellers on generalaviation airplanes. The studyused a sper!ally-developed computerprogramwrittenin BASIC which could comparethe aerodynamic performance of circulation-control propellers with conventional propellers. The comparison of aerodynamic performance for .

circulation-contro l , fixed-pitch and variable-p_tch propellersis basedupon the requirements for a _600 kg (3600Ib) single-engine generalaviationaircraft. A circulation-control propeller usinga supercr'ticalairfoil was shownfeasible o ver a repr e sentative rangeof design c o nditions. At a designconditionfor high sp e ed cruise,all t h reetype so f pr o p e llersshowedapproximately tne same performance.At low speed,the performance of the circu"tion-control propel l er ._xce e d e d t h e p e rformance f o r a fixe d -pitch pr o pellerbut Q ': d not match the " " p e rf o rmance availablefrom a variable-pitch propeller. It appearsfeasibleto _ c o nsidercirculation-control pr o pellers for singleengine aircraftor multi-engine f aircraftwhich have their propellers on a commo , _ axis (tract o r-pusher). The e c o n o m i c s o f the replace m e n t r equ iresa s tudy for each specificairplaneapplication. { , The computerprogramincludeda s the appendixcan be used for generalpurpose _I a e r o dynamic o es ignan d c o mparisons o f perf o rmance.The calculations are ba s ed I u p on w e ll- es ta b l i s hed aer o dynamic relationshi ps for propel lers and wil I accomodate des ign s f o r fix e d-pitch, v ariable-pitch and circulation-control configuratior, s. I 17 . Key W or ds(Sugges t ed by Auth or ll)) 18. Distribu t ionStatement ' , } Ge ne ral Av iation !

Circulation C o ntr o lEffect s )¢ CoanadaEffect Pr o pel ler De._ign !

19. _ ¢urity Cl,siif. (ofthim report] 20. S e curi t yCk.iif. (of this pl _ ) 21. No. of Plgls 22. P r ice _ I U n c la ss ified U nc la ss ifi e d 91 ;